Analysis of delay mean and variance of c
Photon Netw Commun (2011) 21:278–287
DOI 10.1007/s11107-010-0299-2
Analysis of delay mean and variance of collision-free WDM rings
with segment recirculation of blocked traffic
Isaac Seoane · Gerson Rodríguez de los Santos ·
José Alberto Hernández · Manuel Urueña ·
Ricardo Romeral · Ángel Cuevas · David Larrabeiti
Published online: 30 October 2010
© Springer Science+Business Media, LLC 2010
Abstract In Tunable-Transmitter Fixed-Receiver (TT-FR)
-based Wavelength Division Multiplexed (WDM) ring topologies, each node is provided with a dedicated wavelength
(home channel) for reception, which must be shared by the
upstream nodes willing to communicate with it. Thus, to
avoid channel collisions, it is necessary to define a Medium
Access Control (MAC) mechanism that arbitrates access to a
given destination wavelength. This work proposes and analyses a simple MAC mechanism that avoids channel collisions
by recirculating traffic on the upstream ring segment where
congestion was detected. Essentially, whenever a given node
has got any traffic to transmit, it must first block access to
in-transit traffic, which is reflected back to the upstream node
over a second optical fibre. Such blocked traffic is given a
second chance to pass through the congested node after a
round segment delay, thus making use of the ring topology
as buffering units. This work analyses the performance operation of such a MAC protocol under two policies applied to
recirculated traffic: (1) recirculation bypass and (2) recirculation store-and-forward.
Keywords Optical WDM Rings · Tunable-Transmitter
Fixed-Receiver · Collision-free WDM metro rings ·
Teletraffic analysis · Delay mean and variance
1 Introduction and related work
The ever-increasing bandwidth demands of users and applications have made the research community agree that only
I. Seoane · G. R. de los Santos · J. A. Hernández (B) · M. Urueña ·
R. Romeral · Á. Cuevas · D. Larrabeiti
Universidad Carlos III de Madrid, Avda. de la Universidad 30,
28911 Leganés, Madrid, Spain
e-mail: josealberto.hernandez@uc3m.es
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optical fibres and Wavelength Division Multiplexing (WDM)
may provide the solution to meet such demands in the nextgeneration Internet. In light of this, WDM-based architectures have already been proposed for the access, the metro
and the backbone area networks. Concerning the metro area,
the most widely used architecture at present comprises Sonet/SDH rings which combine optical transmission with Time
Division Multiplexed (TDM) switching on every node in the
ring. Thanks to the advent of Reconfigurable Optical AddDrop Multiplexers (ROADMs), more cost-effective WDM
ring technologies have been proposed over the last decade to
replace legacy Sonet/SDH nodes where transit traffic need
not suffer Optical-Electronic-Optical (OEO) conversion and
switching on every intermediate node, but can just traverse
them all-optically. Such architectures require the definition
of new Medium Access Control (MAC) mechanisms to arbitrate channel access since, in most cases, a single wavelength
(or channel) is shared by multiple source nodes and collisions
may occur. This is the case of the so-called Tunable-Transmitter Fixed-Receiver (TT-FR) rings, where each node has
got a dedicated home wavelength for the reception of traffic
and, at the same time, is provided with a fast tunable laser that
allows it to transmit traffic on the dedicated home channel of
other nodes [1,2].
In TT-FR topologies, receiver collisions can never occur
since destination nodes are always listening on their dedicated channel, but transmission collisions may do, since multiple source nodes must compete for accessing the dedicated
home channel of other destination nodes. In this case, the
need for a MAC mechanism that arbitrates channel use is
mandatory to avoid such collisions.
Initial TT-FR WDM ring architectures considered timeslotted bandwidth (with fixed time-slots adjusted to the
maximum packet length) with priority given to in-transit
traffic over locally generated one. Additionally, all nodes
Photon Netw Commun (2011) 21:278–287
were provided with channel inspection capabilities such that
they were able to identify the status (available or occupied)
of forthcoming time-slots and decide whether or not to transmit on them. For instance, the “WDM Multirings” studied
by the authors in [3], proposed a collision-free MAC protocol whereby each node maintains as many separate logical
queues as destination nodes such that, a Synchronous Round
Robin (SRR) protocol scans them sequentially for packet
transmission. This solution reduces the so-called HeadOf-the-Line (HOL) blocking which arises at nodes with a
single FIFO for all destinations where the packet at the head
of the queue blocks access to all wavelengths because it is
destined to a node whose wavelength is always busy. Nevertheless, the authors identified some starvation situations that
may occur and further defined a fairness protocol on top of
SRR to guarantee equal opportunities in accessing the ring.
Such mechanism was further extended in [4] to allow service
differentiation of multiple QoS classes. This architecture and
MAC protocol was finally implemented in a laboratory under
the name of RingO testbed [5].
In parallel, another TT-FR optical ring proposal, called
Hornet, was tested by the authors in [6]. Hornet was originally conceived to employ CSMA/CA as MAC protocol to
avoid transmission collisions [7], but this was soon replaced
by a dedicated control-channel-based MAC whereby a token
advertises the availability of the next time-slots in the future.
Fairness issues are resolved here by limiting the number of
reservations that a given node may make on the token passing
through the out-of-band control channel.
Nevertheless, both RingO and Hornet required slottedtime bandwidth partitioning. Recently, a new MAC protocol
proposed for the Dual Bus Optical Ring Network (DBORN
for short [8]) has shown that it is possible to employ CSMA
with variable packet sizes using cheap passive components,
thus simplifying the optical ring architecture at moderate cost
[9]. This MAC protocol relies on the idea that each node is
provided with a detection window created by delaying transit
traffic by one maximum frame duration using a fibre delay
line (FDL). This gives the node an amount of time enough
to decide whether or not there is a suitable gap in the transit
traffic to schedule the next packet waiting in its local queue.
While this technique is very effective, the fact that transit traffic is given priority over local one may bring serious HOL
problems to downstream nodes, since they can only use the
gaps left in between transit packets.
This work proposes and analyses a novel MAC protocol
that solves channel collisions based on recirculating blocked
traffic over upstream ring segments. In this ring, priority is
given to local traffic over in-transit traffic and, when contention occurs, incoming traffic from upstream nodes are
reflected back to the previous node over a separate fibre in the
opposite direction of data transmission. This way, ring segments are used somehow as buffering devices since blocked
279
traffic is given a second chance to traverse the node found
blocked in the previous attempt. Essentially, giving priority
to local traffic over in-transit traffic gives worse-than-average
access to distant nodes, which translates here to an increase in
the experienced delay. However, as noted before, the opposite
may cause starvation to nodes closely located to the destination node since the available gaps left by transit traffic, after
multiplexed from many source nodes, may be too small to
allocate large packets.
The remainder of this work is thus organised as follows: Sect. 2 explains in detail the proposed architecture and
its operation principles. Sect. 3 analyses the performance
achieved by recirculating traffic over upstream ring segments from a teletraffic perspective. This includes the analysis of the blocking probabilities and delay mean and variance
observed by the packets originated from each node of the
ring. Section 4 validates the performance equations derived
with a Simulink-based experiments and shows a few illustrative example cases. Finally, Sect. 5 concludes this work
reviewing its main contributions and findings.
2 Collision avoidance by recirculating blocked traffic
This section explains the principles of operation of the
bi-directional WDM ring with recirculation of blocked traffic. Figure 1 shows a four-node example of such a bi-directional ring where traffic is assumed to circulate on the clockwise direction over the solid line. Without loss of generality,
let node n 0 be the destination node for local traffic loads
ρi , i = 1, 2, 3 generated by the three upstream nodes n 1 , n 2
and n 3 . Following the TT-FR architecture, such traffic is injected by the transmission nodes on wavelength λ0 , and removed from the ring by the reception node n 0 , which is the
only one capable of listening on λ0 . Additionally, we refer to
links 1+ , 2+ and 3+ (solid lines in the figure) to the optical
fibres connecting node pairs 0–1, 1–2 and 2–3 respectively
in the clockwise (regular transmission) direction, and denote
1− , 2− and 3− (dashed lines in the figure) the optical fibres connecting the same node pairs 0–1, 1–2 and 2–3 in the
counter-clockwise direction. Finally, it is clear that traffic injected on the ring by node n 3 must first traverse nodes n 2 and
n 1 respectively to reach its destination node n 0 ; traffic generated at node n 2 must go through node n 1 before reaching the
destination node, and traffic generated at node n 1 does not
traverse any intermediate node, since it is directly attached
to node n 0 by segment 1+ .
Basically, when a given node has any traffic to transmit
to node n 0 , before doing so, it must check the availability
of this wavelength and then block access to channel λ0 in
order to prevent collisions with in-transit traffic from
upstream nodes. Blocking such access means that any incoming traffic from upstream nodes is redirected back to the
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Clearly, packets are expected to experience less endto-end delay in the first case since they do not suffer OEO conversion upon reaching a blocked node. However, too many
recirculations of traffic may cause the signal to noise ratio
degrade significantly with subsequent data loss. Essentially,
recirculation bypass of blocked traffic is preferred at low
loads (few recirculation times) but, at high loads, when data
packets are expected to recirculate several times, conversion
to the electronic domain might be mandatory. Additionally,
when segment lengths are too large with subsequent high
attenuation losses, store and forward might be preferred for
signal’s regeneration purposes. Nevertheless, in both cases,
the ring segments act somehow as optical buffering elements.
The next section studies the delay mean and variance experienced in both cases.
3 Analysis
Fig. 1 A four-node WDM ring with recirculation of blocked traffic.
Notation of traffic flow intensities
previous node through the counter-clockwise fibre (dashed
fibre link). Such blocked and redirected traffic, when arriving
at the previous (upstream) node can be treated following one
of two different policies, as illustrated in Fig. 2a, b:
• Recirculation bypass (Fig. 2a): In this case, recirculated
traffic has got priority over local traffic and it bypasses
the previous node directly to the blocked node without
any OEO conversion. In case there is local traffic waiting
for transmission, this must wait.
• Recirculation store-and-forward (Fig. 2b): In this case,
recirculated traffic is converted to the electronic domain
and must wait in queue together with local traffic. No
priority is given to recirculated traffic.
Fig. 2 Recirculation bypass
(left) and store and forward
(right). a Recirculation Bypass
b Recirculation
store-and-forward
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Let N + 1 refer to the number of nodes in the ring of Fig. 1,
and let n i , i = 0, . . . , N be used to label each node in the
optical ring. Without loss of generality, the aim is to study
the delay experienced by the packets injected by any source
node n i with i = 1, . . . , N to the destination node n 0 , both
under the recirculation bypass and the recirculation storeand-forward policies. The following blocking analysis holds
for both policies.
3.1 Blocking analysis
As previously stated, each node is provided with a dedicated
home channel for reception, in this case, node n 0 continuously listens on wavelength λ0 . Thus, upstream nodes must
compete for accessing λ0 . Now, let ρi refer to the traffic load
that node n i offers to wavelength λ0 (that is, destined to node
n 0 ). In addition to this, ρi,o f f refers to the total amount of
traffic offered on segment i + , which basically comprises a
sum of traffic load intensities. Owing to the flow conservation
law on each node, the sum of incoming flow intensities must
equal the sum of outgoing flow intensities. This translates to
the following set of N + 1 equations:
Photon Netw Commun (2011) 21:278–287
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ρout + ρ1,o f f B0 = ρ1,o f f
⇒ ρout = ρ1,o f f (1 − B0 )
ρ1,o f f + ρ2,o f f B1 = ρ1 + ρ2,o f f + ρ1,o f f B0
⇒ ρ1,o f f (1 − B0 ) = ρ1 + ρ2,o f f (1 − B1 )
ρ2,o f f + ρ3,o f f B2 = ρ2 + ρ3,o f f + ρ2,o f f B1
⇒ ρ2,o f f (1 − B1 ) = ρ2 + ρ3,o f f (1 − B2 )
.. .. ..
. . .
ρ N ,o f f = ρ N + ρ N ,o f f B N −1
⇒ ρ N ,o f f (1 − B N −1 ) = ρ N
where ρi+1,o f f Bi refers to the amount of traffic offered to
node i and blocked at this node (with probability Bi ).
It can be easily shown from the equations above that:
ρout = ρ1,o f f (1 − B0 ) = ρ1 + ρ2,o f f (1 − B1 )
= ρ1 + ρ2 + ρ3,o f f (1 − B2 ) = . . .
= ρ1 + ρ2 + · · · + ρ N ,o f f (1 − B N −1 )
=
N
(1)
ρi
i=1
which confirms that no data is lost (flow conservation law),
that is, all traffic injected in the network eventually arrives at
node n 0 .
N
ρi , the values of the offered trafGiven that ρout = i=1
fic ρi,o f f on each node are derived as:
ρ1,o f f =
N
1
ρout
=
ρi
1 − B0
1 − B0
E B (ρ, M) =
ρM
M!
M ρ j
j=0 j!
(4)
Thus, using Eq. 2 for ρi,o f f , the above Eq. 3 yields:
Bi−1 N
ρi + 1−B
k=i ρk
i−1
, i = 1, . . . , N
Bi =
Bi−1
N
1 + ρi + 1−B
k=i ρk
i−1
(5)
with B0 = 0 since the destination node is never blocked
because it never injects traffic on λ0 .
Thus, given a set of traffic intensities ρi destined to node
n 0 , it is very easy to compute the blocking probabilities Bi
from Eq. 5 recursively, that is: starting from B0 = 0, then
B0 N
B1 = ρ1 + 1−B
i=1 ρi = ρ1 , and so on. The next step
0
is to derive the amount of time required by each packet to
successfully arrive at the destination node following the two
recirculation policies: (1) store and forward and (2) bypass.
3.2 Delay analysis
i=1
ρ2,o f f =
N
ρ1,o f f (1 − B0 ) − ρ1
1
=
ρi
1 − B1
1 − B1
3.2.1 Recirculation store-and-forward
i=2
ρ3,o f f
ρ2,o f f (1 − B1 ) − ρ2
1
=
=
1 − B2
1 − B2
N
ρi
i=3
.. .. ..
. . .
ρ N −1,o f f (1 − B N −2 ) − ρ N −1
1
=
ρN
ρ N ,o f f =
1 − B N −1
1 − B N −1
So, in general, for node n i :
ρi,o f f =
N
1
ρk , i = 1, . . . , N
1 − Bi−1
(2)
k=i
This information is very useful for computing the blocking probabilities Bi experienced by transit traffic on each
node n i , using the well-known Erlang-loss equations. Essentially, the blocking probability experienced by transit traffic
on every node follows:
Bi = E B (ρi + ρi,o f f Bi−1 , 1), i = 1, . . . , N
(3)
where E B (ρ, M) refers to the Erlang-B loss equation of ρ
units of traffic to be served by M circuits. Remark that:
In this case, data frames arriving at a blocked node need
to travel back to the previous node in the ring, where they
suffer OE conversion and wait in queue together with the
node’s traffic load. Thus, assuming infinite buffer queues, no
buffer overflow occurs and all data frames eventually arrive at
their destination. However, data frames may need to recirculate several times certain segments if these are usually found
blocked, with subsequent unbounded delay. Thus, it is important to study both the delay mean and its variance to give an
idea of not only the average delay experienced on the ring
but also the jitter.
Under the assumption of unlimited electronic buffering,
the results of queueing theory for M/M/1 systems apply to
derive the average delay experienced at each node’s queue,
namely E(Q i ), i = 1, . . . , N . This value is given by:
E(Q i ) =
E(S)
1 − ρi
(6)
where E(S) is the average service time of a data frame of size
E(B) bits transmitted over a link of capacity C bits/s. In other
words: E(S) = E(B)/C. For a typical 1500-byte data frame
over a 10-Gbps link, this is, E(S) = 1500 · 8/1010 = 1.2 µs.
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Photon Netw Commun (2011) 21:278–287
Now, let loop j refer to the segments j + and j − . Thus, a
given packet originated at node nl and destined to node n 0
experiences the following delay:
Dl = Q l + Reo +
l
L j + Roe
(7)
j=1
which accounts for the queueing delay experienced until it
is injected on the ring plus the amount of time L j spent on
each intermediate loop j, with j = 0, . . . , l − 1. Additionally, the EO and OE conversion delays (Reo and Roe in Eq. 2)
suffered when entering and exiting the ring respectively are
also considered in the model.
Now, consider loop j only: If the packet finds node n j
free (which occurs with probability 1 − B j ), then the packet
only suffers propagation delay R j . Otherwise, this packet
is reflected back to node n j+1 , converted to electronic, and
stored in the queue of node j +1 (this occurs with probability
B j ). In the next attempt, if the packet finds node n j free, then
the packet has experienced a total delay of 2R j + Q j+1 + R j
(this is with probability B j (1 − B j )). If the packet is successfully transmitted on the third attempt (with probability
B 2j (1 − B j ), then such packet experiences a total delay of
4R j + 2Q j+1 + R j , and so on. Following this reasoning,
the total delay experienced by a packet traversing loop j is
given by:
m
2R j + Roe + Q j+1 + Reo
L j = Rj +
the OE and EO conversion which are fixed quantities, i.e.
E(Roe ) = Roe and E(Roe ) = Roe . The loop’s delay variance V ar (L j ) is given by1 :
V ar (L j ) = V ar (R j )
+E(m)V ar (2R j + Roe + Q j+1 + Reo )
+(E(2R j + Roe + Q j+1 + Reo ))2 V ar (m)
Bj
Bj
V ar (Q j+1 ) +
=
1 − Bj
(1 − B j )2
2
× 2R j + Roe + E(Q j+1 ) + Reo
(11)
where V ar (R j ) = 0 since the propagation delay is a
fixed value. The same reasoning applies to V ar (Roe ) =
2
E(S)
.
V ar (Reo ) = 0. Additionally, V ar (Q j+1 ) = 1−ρ
j
Finally, the end-to-end delay experienced by a packet originated at node nl has got the following mean and variance:
l−1
1+B j
E(S)
Rj
+Reo +
E(Dl ) =
1−ρl
1−B j
j=0
Bj
+ Roe
+(Reo +E(Q j+1 )+Roe )
1−B j
l−1
Bj
E(S) 2
V ar (Dl ) =
+
V ar (Q j+1 )
1−ρl
1−B j
j=0
+
(8)
Bj
(1−B j )2
k=0
2
2R j +Reo +E(Q j+1 )+Roe
where m is a geometrically distributed random variable with
parameter B j . Essentially, m gives the number of extra
attempts required for the successful transmission of a given
packet over loop j, characterised by the probability B j to
find the next node n j blocked in the end-to-end path. In other
words:
3.2.2 Recirculation bypass
P(m = k) = (1 − B j )B kj , k = 0, 1, . . .
In this case, the same Eq. 2 as above applies here:
(9)
Additionally, it is worth remarking from Eq. 8 that packets must suffer OE and EO delay whenever they find the next
node blocked, since they must be electronically buffered on
the immediate upstream node.
The mean delay for loop L j is given by:
E(L j ) = E(R j )+E(m)E(2R j +Roe +Q j+1 +Reo )
Bj
2E(R j )+E(Roe )+E(Q j+1 )
= E(R j )+
1 − Bj
+ E(Reo ))
Bj
1+B j
= Rj
+(Roe +E(Q j+1 )+Reo )
(10)
1 − Bj
1 − Bj
where E(R j ) = R j since the propagation delay is a fixed
value given by the fibre length and the speed of light on
the optical fibre (typically 2 · 108 m/s). The same applies to
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(12)
(13)
under the assumption of node independency.
As shown, at low load levels, a given packet originated at
node l would ideally experience a delay of E(Q l )+ l−1
j=0 R j .
Dl = Q l + Reo +
l
L j + Roe
(14)
j=1
However, the computation of Q l and L j is rather different.
First of all, the delay experienced on the j-th loop, L j , does
not include queueing delay since, recirculated traffic does not
suffer OEO conversion and queueing on the previous nodes.
Thus:
L j = Rj +
m
2R j
(15)
k=0
1 Remark that the variance of a random sum of N iid random variN
X i ) = E(N )V ar (X 1 ) +
ables X i , i = 1, 2, . . . is given by: V ar ( i=1
2
E (X 1 )V ar (N ).
Photon Netw Commun (2011) 21:278–287
283
In addition, the average queueing delay experienced by the
packets before entering the ring is also different from the
previous case:
E(Q i ) =
E(S)
(1 − ρi )(1 − Bi−1 )
(16)
Since the capacity observed by the queue on node n i is
only the remaining one left by the recirculated traffic, that is,
C(1 − Bi−1 ).
Thus, the mean delay and variance experienced by packets
on loop L j are given by:
E(L j ) = E(R j ) + E(m)E(2R j )
Bj
1 + Bj
2E(R j ) = R j
= E(R j ) +
1 − Bj
1 − Bj
1 µs
= 1.0526 µs
1 − 0.05
60/8 km
= 37.5 µs
2 · 105 km/s
(17)
R=
(18)
Clearly, the total delay depends on the number of segments
that a given packet must traverse until reaching its destination
(its relative position in the ring) and the number of times that
such a packet must recirculate each segment (which depends
on the blocking probabilities) before reaching their destination. Additionally, the values of Roe and Reo may also
comprise a significant portion of it.
The next section explores such average delay and its variance on different topologies and under uniform and nonuniform traffic loads.
V ar (L j ) = V ar (R j ) + E(m)V ar (2R j )
where V ar (R j ) = 0 since the propagation delay is a fixed
2
E(S)
.
value. Additionally, V ar (Q j+1 ) = 1−ρ
j
Finally, the end-to-end delay mean and variance for packets under the recirculation bypass strategy is given by:
E(S)
+ Reo
(1 − ρl )(1 − Bl−1 )
l−1
1 + Bj
+ Roe
Rj
+
1 − Bj
j=0
2
E(S)
V ar (Dl ) =
(1 − ρl )(1 − Bl−1 )
l−1
Bj
2
4
+
R
(1 − B j )2 j
E(Q) =
and suffer the following propagation delay per segment:
and
+(E(2R j ))2 V ar (m)
Bj
=
(2R j )2
(1 − B j )2
where ρ denotes the input queue load. Finally, both OE and
EO delays have been assumed Roe = Reo = 25 µs.
To give an example with real numbers in the recirculation store-and-forward policy, let the ring comprise N + 1 =
8 nodes equally spaced on a 60 km long ring. Also, let all
nodes operate under the same traffic load ρ = 0.05, then the
queueing delay experienced by a packet to enter the ring is
given by:
4.1 Analysis validation via simulation
E(Dl ) =
(19)
(20)
j=0
again under the assumption of node independency.
4 Numerical examples
This section aims to validate the analytical equations derived
above and perform a few simulation scenarios to determine
what aspects have a greater impact on delay and jitter in the
ring. The scenario considers a 60- km ring with N + 1 nodes
labelled n 0 to n N with node n 0 acting as destination node. The
size of packets injected in the ring is exponentially-distributed with mean E(B) = 1250 bytes, thus giving an average
= 1 µs on a C = 10 Gbps
service time: E(S) = 1250×8
10·109
interface. Additionally, nodes are assumed to aggregate traffic from multiple users, leading to traffic profile injected in
the ring that follows a Poisson process with rate λ = ρ/E(S),
This first experiment validates the delay equations derived
through the analysis section with simulation. The simulation was developed in Matlab’s Simulink for a 60- km ring
with N + 1 = 8 nodes at different input loads, and assuming the values of capacity C = 10 Gbps, E(B) = 1250
bytes and Roe = Reo = 25 µs, as described above. It is also
worth remarking that the maximum input load per node is
ρmax = 1/(N + 1), since the maximum offered load on the
last segment must not exceed unity.
Figure 3 shows both the analytical and simulated results
for such a ring, assuming both policies upon blocked traffic: Recirculation store-and-forward (top) and recirculation
bypass (bottom). For brevity purposes, only the delay experienced by the first and the last nodes in the ring, together with
the node in the middle, are depicted. As noted, both analytical and simulated values accurately match one another both
in terms of delay mean (dots) and standard deviation (error
bars), at different traffic loads. The reader must note that the
error bars represent the standard deviation of delay (not confidence intervals) in units of time. In this case, the maximum
input load per node is ρmax = 1/(N + 1) = 0.125.
The next experiments consider only the analytical results
to show the benefits and shortcomings of the two policies
(Recirculation bypass and store-and-forward) on different
scenarios.
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Photon Netw Commun (2011) 21:278–287
N=8, Recirculation Store−and−Forward
N=8, Recirculation Store−and−Forward Simulated
700
E2E delay (µs)
E2E delay (µs)
700
600
500
400
300
200
100
0
0
600
500
400
300
200
100
0.02
0.04
0.06
0.08
0.1
0
0
0.12
0.02
0.04
Load ρ
400
400
300
200
100
0.04
0.06
0.1
0.12
N=8, Recirculation Bypass Simulated
500
E2E delay (µs)
E2E delay (µs)
N=8, Recirculation Bypass
0.02
0.08
Load ρ
500
0
0
0.06
0.08
0.1
300
200
100
0
0
0.12
0.02
Load ρ
0.04
0.06
0.08
0.1
0.12
Load ρ
Last node
Half−distant node
First node
Fig. 3 Analysis validation with Matlab’s Simulink for a network with N = 8 nodes. Analytical results (on the left) and Simulation results (on the
right) are obtained assuming recirculation Store-and-Forward (top) and recirculation bypass (bottom)
4.2 Delay analysis for different values of N
This experiment provides a comparison between the two policies when the number of nodes in the ring varies. Remark
that the ring length is 60- km fixed and the values for E(B) =
1250 bytes, C = 10 Gbps and Roe = Reo = 25 µs are the
same as before. Two cases are considered: (a) N + 1 = 8 and
(b) N + 1 = 32. In the first case, the propagation delay per
3 /8
= 37.5 µs whereas in the second
segment is R = 60·10
2·108
3
/32
= 9.37 µs. The average delay and
case this is R = 60·10
2·108
variance is given in Fig. 4 for the two cases at different link
loads. Again for brevity, only the first, last and a node in the
middle of the ring are plotted.
As shown in the figure, there is a great performance difference (in terms of delay mean and variance) between the
recirculation bypass and the recirculation store-and-forward
policies, in both cases, especially at high loads. In all cases,
the recirculation bypass policy for blocked frames is shown
to reduce the average delay experienced by packets and its
variance since these do not suffer OEO conversion. Additionally we can note the following conclusions:
• The first node does not experience a big difference in
terms of delay mean and variance in all cases. This is
because the closest nodes perceive a high-priority treat-
123
ment with respect to last nodes, thus experiencing only
about R + Roe + Reo in most cases.
• At low loads, there is no big difference between the average delay experienced by packets in the two policies, but
there is when it comes to variance (jitter).
• When the recirculation bypass technique is used, there
is no big difference in terms of average delay between a
60- km ring with 8 or 32 nodes, but there is in terms of
variance. This is an important conclusion to keep in mind
when upgrading a fixed-length ring with more intermediate nodes.
• The opposite conclusion occurs in the recirculation storeand-forward technique since it is shown that there is not a
big difference in terms of variance when upgrading from
8 to 32 nodes, but there is some difference in terms of
average delay.
4.3 Delay analysis when one node offers a peak of traffic
Figure 5 shows the delay mean and variance observed on each
node in the ring assuming that a given node abuses from the
network resources. In this experiment, all nodes are assumed
lightly loaded (ρ = 0.0312) except a misbehaving one which
transmits an amount of traffic equal to ρpeak = 0.75. As
shown, when this occurs, the effect observed is that this misbehaving node blocks access to the previous ones in the ring,
Photon Netw Commun (2011) 21:278–287
285
N=8, Recirculation bypass
600
500
500
E2E delay (µs)
E2E delay (µs)
N=8, Recirculation Store−and−Forward
600
400
300
200
100
0
0
0.02
0.04
0.06
0.08
0.1
400
300
200
100
0
0
0.12
0.02
0.04
Load ρ
500
500
400
300
200
100
0.005
0.01
0.015
0.08
0.1
0.12
N=32, Recirculation bypass
600
E2E delay (µs)
E2E delay (µs)
N=32, Recirculation Store−and−Forward
600
0
0
0.06
Load ρ
0.02
0.025
400
300
200
100
0
0
0.03
0.005
0.01
Load ρ
0.015
0.02
0.025
0.03
Load ρ
Half−distant node
Last node
First node
Fig. 4 Delay mean and variance experienced by packets in the two policies for variable number of nodes N + 1
Peak on node 1
Peak on node 1
700
700
Recirculation Store−and−Forward
Recirculation bypass
600
E2E delay (µs)
E2E delay (µs)
600
500
400
300
200
100
0
0
500
400
300
200
100
1
2
3
4
5
6
0
0
7
1
2
Node index
Peak on node 5
5
6
7
5
6
7
700
Recirculation Store−and−Forward
Recirculation bypass
600
E2E delay (µs)
600
E2E delay (µs)
4
Peak on node 5
700
500
400
300
200
100
0
0
3
Node index
500
400
300
200
100
1
2
3
4
5
6
7
Node index
0
0
1
2
3
4
Node index
Fig. 5 Delay mean and variance on each node assuming a peak of traffic on nodes n 1 (top) and on node n 6 (bottom) on an 8-node WDM ring
thus increasing very significantly their delay mean and especially their variance. This is particularly harmful in the recirculation store-and-forward case, where the nodes before the
misbehaving one experience a significant increase in their
delay and variance due to multiple OEO conversions and
queueing. When employing recirculation bypass, node abuse
is specially harmful in terms of delay variance, rather than
by means of delay mean.
123
286
5 Conclusions
This work has proposed a novel MAC protocol to avoid channel collisions in TT-FR-based WDM rings. The novelty introduced by this MAC protocol is that blocked traffic is recirculated back to upstream nodes, where they can be directly
forwarded to the next node (Recirculation bypass) or stored
in queue and be forwarded next (Recirculation store-andforward). In both cases, the delay mean and variance experienced by the packets are analysed to show the difference in
terms of performance in both cases. The experiments reveal
that the recirculation store-and-forward introduces more delay to packets than recirculation bypass, especially at high
traffic loads and, more significantly, a tremendous delay variance, which is very harmful for real-time traffic. Such a
model can be used to further study the impact of both policies on traffic demanding strict QoS requirements.
Acknowledgments The work described in this paper was carried out
with the support of the BONE project (“Building the Future Optical
Network in Europe”), a Network of Excellence funded by the European
Commission through the 7th ICT-Framework Programme. Additionally, the authors would like to thank the support of the T2C2 Spanish
project (under code TIN2008-06739-C04-01) to the development of
this work.
References
[1] Chlamtac, I., Fumagalli, A., Kazovsky, L.G., Poggiolini, P.:
A multi-Gbit/s WDM optical packet network with physical ring
topology and multi sub-carrier header encoding. In: Proceedings
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[2] Marsan, M.A., Fumagalli, A., Leonardi, E., Neri, F.: R-daisy: an alloptical packet network. In: Proceedings of European Symposium
on Advanced Networks and Services, March 1995
[3] Marsan, M.A., Bianco, A., Leonardi, E., Meo, M., Neri, F.: MAC
protocols and fairness control in WDM multirings with tunable
transmitters and fixed receivers. IEEE/OSA J. Lightwave Technol. 14(6), 1230–1244 (1996)
[4] Marsan, M.A., Bianco, A., Leonardi, E., Morabito, A., Neri, F.: Alloptical WDM multi-rings with differentiated QoS. IEEE Commu.
Mag. 37(2), 58–66 (1999)
[5] Carena, A., de Feo, V., Finochietto, J.M., Gaudino, R., Neri, F.,
Piglione, C., Poggiolini, P.: RingO: an experimental WDM optical
packet network for metro applications. IEEE J. Sel. Areas Commun. 22(8), 1561–1571 (2004)
[6] White, I.M., Rogge, M.S., Shrikhande, K., Kazovsky, L.G.: A summary of the HORNET projetc: a next-generation metropolitan area
network. IEEE J. Sel. Areas Commun. 21(9), 1478–1494 (2003)
[7] Kim, K.S., Okagawa, H., Shrikhande, K., Kazovsky, L.G.: Unslotted optical CSMA/CA MAC protocol with fairness control in metro
WDM ring networks. In: Proceedings of IEEE Globecom, vol. 3,
pp. 2370–2374, Nov 2002
[8] Bouandallah, N., Beylot, A.L., Dotaro, E., Pujolle, G.: Resolving
the fairness issues in bus-based optical access networks. IEEE J.
Sel. Areas Commun. 23(8), 1444–1457 (2005)
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[9] Bouabdallah, N., Perros, H.: Cost-effective single-hub WDM ring
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3901 (2007)
Author Biographies
Isaac Seoane received the Telecommunications Engineering degree in 2004 and the
M.Sc. in Telematics Engineering in 2007 at
Universidad Carlos III de Madrid (Spain).
He is an assistant lecturer and researcher at
the Department of Telematic Engineering at
Universidad Carlos III de Madrid (Spain)
since 2006 where he has participated in several national and European researching projects, such as IMPROVISA, T2C2, and the EU-funded e-Photon/ONe+,
BONE and Indect. He is currently working on his Ph.D. Thesis about
optical ring networks and also doing research in some other networking-related topics such as emergency networks, multipath and multiple
description for multimedia content.
Gerson Rodríguez de los Santos received
his Telecommunications Engineering degree
in April 2008 and is pursuing the M.Sc.
in Telematics Engineering at Universidad
Carlos III de Madrid (Spain). He is currently working at Universidad Carlos III as a
research assistant, providing technical support for a number of both national and european research projects (INDECT, BONE,
PASITO, T2C2, etc). His research interests cover the fields of Optical
Transparent Networks, Network Hardware development and Switching
in general. He is also pursuing the Ph.D. degree in Telematic Engineering at the aforementioned University.
José Alberto Hernández completed the
five-year degree in Telecommunications
Engineering at Universidad Carlos III de
Madrid (Madrid, Spain) in 2002, and the
Ph.D. degree in Computer Science at Loughborough University (Leics, United Kingdom)
in 2005. From 2005 to 2009, he was a postdoctoral research and teaching assistant at
Universidad Autónoma de Madrid, where he
participated in a number of both national and european research projects
concerning the modeling and performance evaluation of communication networks, and particularly the optical burst switching technology.
In 2009, he moved to Universidad Carlos III de Madrid, where he currently works as a visiting lecturer and senior researcher, with more than
40 articles published in both journals and conference in-proceedings.
His research interests include the areas at which mathematical modeling and computer networks overlap.
Manuel Urueña received the M.Sc. degree
in Computer Science in 2001 from Universidad Politécnica de Madrid and the Ph.D. in
Telecommunications in 2005 from Universidad Carlos III de Madrid. At present, he is
an assistant professor of Telematics engineering at Universidad Carlos III de Madrid. His
research activities range from P2P systems,
through load balancing and service discovery
protocols, to Optical networks. He has been involved in international
and national research projects related with these topics, including the
EU IST GCAP and the EU SEC INDECT projects.
Photon Netw Commun (2011) 21:278–287
Ricardo Romeral obtained his M.Sc. degree in Telecommunications Engineering and
his Ph.D. in Telemeatics Engineering from
Universidad Carlos III de Madrid (Spain) in
2001 and 2007 respectively. Dr. Romeral is
an assistant professor at Universidad Carlos
III de Madrid since then, where he combines
lecturing and research in the fields of network
measuring and monitoring, GMPLS and optical networks, among many others. He has collaborated in several European and Spanish projects related to traffic monitoring and analysis in
optical backbone networks, and programmable networking.
Ángel Cuevas received his M.Sc. in Telecommunication Engineering and M.Sc. in
Telematic Engineering at Universidad Carlos
III de Madrid in 2006 and 2007, respectively.
He was awarded with an Erasmus Scholarship and complete his Master Thesis at
The University of Reading. Currently he is
Ph.D. Candidate at the Department of Telematic Engineering at University Carlos III de
Madrid. Also, he held a research Internship at SAP Labs France. His
research interests include Wireless Sensor Networks, Overlay and P2P
Networks and Optical Networks.
287
David Larrabeiti [M’96] is currently a full
professor at Universidad Carlos III de Madrid
(Spain) since 1998, where he teaches several modules concerning high-speed switching networks and architectures. He received
the M.Sc. and Ph.D. degrees in Telecommunications Engineering from Universidad
Politécnica de Madrid in 1991 and 1996
respectively. He has participated in a large
number of both national and international research projects focused on
next-generation networks for more than a decade. His research interests
include the design of the future Internet infrastructure, ultra-broadband
multimedia transport, and traffic engineering over IP-GMPLS backbones. His email address is dlarra@it.uc3m.es.
123
DOI 10.1007/s11107-010-0299-2
Analysis of delay mean and variance of collision-free WDM rings
with segment recirculation of blocked traffic
Isaac Seoane · Gerson Rodríguez de los Santos ·
José Alberto Hernández · Manuel Urueña ·
Ricardo Romeral · Ángel Cuevas · David Larrabeiti
Published online: 30 October 2010
© Springer Science+Business Media, LLC 2010
Abstract In Tunable-Transmitter Fixed-Receiver (TT-FR)
-based Wavelength Division Multiplexed (WDM) ring topologies, each node is provided with a dedicated wavelength
(home channel) for reception, which must be shared by the
upstream nodes willing to communicate with it. Thus, to
avoid channel collisions, it is necessary to define a Medium
Access Control (MAC) mechanism that arbitrates access to a
given destination wavelength. This work proposes and analyses a simple MAC mechanism that avoids channel collisions
by recirculating traffic on the upstream ring segment where
congestion was detected. Essentially, whenever a given node
has got any traffic to transmit, it must first block access to
in-transit traffic, which is reflected back to the upstream node
over a second optical fibre. Such blocked traffic is given a
second chance to pass through the congested node after a
round segment delay, thus making use of the ring topology
as buffering units. This work analyses the performance operation of such a MAC protocol under two policies applied to
recirculated traffic: (1) recirculation bypass and (2) recirculation store-and-forward.
Keywords Optical WDM Rings · Tunable-Transmitter
Fixed-Receiver · Collision-free WDM metro rings ·
Teletraffic analysis · Delay mean and variance
1 Introduction and related work
The ever-increasing bandwidth demands of users and applications have made the research community agree that only
I. Seoane · G. R. de los Santos · J. A. Hernández (B) · M. Urueña ·
R. Romeral · Á. Cuevas · D. Larrabeiti
Universidad Carlos III de Madrid, Avda. de la Universidad 30,
28911 Leganés, Madrid, Spain
e-mail: josealberto.hernandez@uc3m.es
123
optical fibres and Wavelength Division Multiplexing (WDM)
may provide the solution to meet such demands in the nextgeneration Internet. In light of this, WDM-based architectures have already been proposed for the access, the metro
and the backbone area networks. Concerning the metro area,
the most widely used architecture at present comprises Sonet/SDH rings which combine optical transmission with Time
Division Multiplexed (TDM) switching on every node in the
ring. Thanks to the advent of Reconfigurable Optical AddDrop Multiplexers (ROADMs), more cost-effective WDM
ring technologies have been proposed over the last decade to
replace legacy Sonet/SDH nodes where transit traffic need
not suffer Optical-Electronic-Optical (OEO) conversion and
switching on every intermediate node, but can just traverse
them all-optically. Such architectures require the definition
of new Medium Access Control (MAC) mechanisms to arbitrate channel access since, in most cases, a single wavelength
(or channel) is shared by multiple source nodes and collisions
may occur. This is the case of the so-called Tunable-Transmitter Fixed-Receiver (TT-FR) rings, where each node has
got a dedicated home wavelength for the reception of traffic
and, at the same time, is provided with a fast tunable laser that
allows it to transmit traffic on the dedicated home channel of
other nodes [1,2].
In TT-FR topologies, receiver collisions can never occur
since destination nodes are always listening on their dedicated channel, but transmission collisions may do, since multiple source nodes must compete for accessing the dedicated
home channel of other destination nodes. In this case, the
need for a MAC mechanism that arbitrates channel use is
mandatory to avoid such collisions.
Initial TT-FR WDM ring architectures considered timeslotted bandwidth (with fixed time-slots adjusted to the
maximum packet length) with priority given to in-transit
traffic over locally generated one. Additionally, all nodes
Photon Netw Commun (2011) 21:278–287
were provided with channel inspection capabilities such that
they were able to identify the status (available or occupied)
of forthcoming time-slots and decide whether or not to transmit on them. For instance, the “WDM Multirings” studied
by the authors in [3], proposed a collision-free MAC protocol whereby each node maintains as many separate logical
queues as destination nodes such that, a Synchronous Round
Robin (SRR) protocol scans them sequentially for packet
transmission. This solution reduces the so-called HeadOf-the-Line (HOL) blocking which arises at nodes with a
single FIFO for all destinations where the packet at the head
of the queue blocks access to all wavelengths because it is
destined to a node whose wavelength is always busy. Nevertheless, the authors identified some starvation situations that
may occur and further defined a fairness protocol on top of
SRR to guarantee equal opportunities in accessing the ring.
Such mechanism was further extended in [4] to allow service
differentiation of multiple QoS classes. This architecture and
MAC protocol was finally implemented in a laboratory under
the name of RingO testbed [5].
In parallel, another TT-FR optical ring proposal, called
Hornet, was tested by the authors in [6]. Hornet was originally conceived to employ CSMA/CA as MAC protocol to
avoid transmission collisions [7], but this was soon replaced
by a dedicated control-channel-based MAC whereby a token
advertises the availability of the next time-slots in the future.
Fairness issues are resolved here by limiting the number of
reservations that a given node may make on the token passing
through the out-of-band control channel.
Nevertheless, both RingO and Hornet required slottedtime bandwidth partitioning. Recently, a new MAC protocol
proposed for the Dual Bus Optical Ring Network (DBORN
for short [8]) has shown that it is possible to employ CSMA
with variable packet sizes using cheap passive components,
thus simplifying the optical ring architecture at moderate cost
[9]. This MAC protocol relies on the idea that each node is
provided with a detection window created by delaying transit
traffic by one maximum frame duration using a fibre delay
line (FDL). This gives the node an amount of time enough
to decide whether or not there is a suitable gap in the transit
traffic to schedule the next packet waiting in its local queue.
While this technique is very effective, the fact that transit traffic is given priority over local one may bring serious HOL
problems to downstream nodes, since they can only use the
gaps left in between transit packets.
This work proposes and analyses a novel MAC protocol
that solves channel collisions based on recirculating blocked
traffic over upstream ring segments. In this ring, priority is
given to local traffic over in-transit traffic and, when contention occurs, incoming traffic from upstream nodes are
reflected back to the previous node over a separate fibre in the
opposite direction of data transmission. This way, ring segments are used somehow as buffering devices since blocked
279
traffic is given a second chance to traverse the node found
blocked in the previous attempt. Essentially, giving priority
to local traffic over in-transit traffic gives worse-than-average
access to distant nodes, which translates here to an increase in
the experienced delay. However, as noted before, the opposite
may cause starvation to nodes closely located to the destination node since the available gaps left by transit traffic, after
multiplexed from many source nodes, may be too small to
allocate large packets.
The remainder of this work is thus organised as follows: Sect. 2 explains in detail the proposed architecture and
its operation principles. Sect. 3 analyses the performance
achieved by recirculating traffic over upstream ring segments from a teletraffic perspective. This includes the analysis of the blocking probabilities and delay mean and variance
observed by the packets originated from each node of the
ring. Section 4 validates the performance equations derived
with a Simulink-based experiments and shows a few illustrative example cases. Finally, Sect. 5 concludes this work
reviewing its main contributions and findings.
2 Collision avoidance by recirculating blocked traffic
This section explains the principles of operation of the
bi-directional WDM ring with recirculation of blocked traffic. Figure 1 shows a four-node example of such a bi-directional ring where traffic is assumed to circulate on the clockwise direction over the solid line. Without loss of generality,
let node n 0 be the destination node for local traffic loads
ρi , i = 1, 2, 3 generated by the three upstream nodes n 1 , n 2
and n 3 . Following the TT-FR architecture, such traffic is injected by the transmission nodes on wavelength λ0 , and removed from the ring by the reception node n 0 , which is the
only one capable of listening on λ0 . Additionally, we refer to
links 1+ , 2+ and 3+ (solid lines in the figure) to the optical
fibres connecting node pairs 0–1, 1–2 and 2–3 respectively
in the clockwise (regular transmission) direction, and denote
1− , 2− and 3− (dashed lines in the figure) the optical fibres connecting the same node pairs 0–1, 1–2 and 2–3 in the
counter-clockwise direction. Finally, it is clear that traffic injected on the ring by node n 3 must first traverse nodes n 2 and
n 1 respectively to reach its destination node n 0 ; traffic generated at node n 2 must go through node n 1 before reaching the
destination node, and traffic generated at node n 1 does not
traverse any intermediate node, since it is directly attached
to node n 0 by segment 1+ .
Basically, when a given node has any traffic to transmit
to node n 0 , before doing so, it must check the availability
of this wavelength and then block access to channel λ0 in
order to prevent collisions with in-transit traffic from
upstream nodes. Blocking such access means that any incoming traffic from upstream nodes is redirected back to the
123
280
Photon Netw Commun (2011) 21:278–287
Clearly, packets are expected to experience less endto-end delay in the first case since they do not suffer OEO conversion upon reaching a blocked node. However, too many
recirculations of traffic may cause the signal to noise ratio
degrade significantly with subsequent data loss. Essentially,
recirculation bypass of blocked traffic is preferred at low
loads (few recirculation times) but, at high loads, when data
packets are expected to recirculate several times, conversion
to the electronic domain might be mandatory. Additionally,
when segment lengths are too large with subsequent high
attenuation losses, store and forward might be preferred for
signal’s regeneration purposes. Nevertheless, in both cases,
the ring segments act somehow as optical buffering elements.
The next section studies the delay mean and variance experienced in both cases.
3 Analysis
Fig. 1 A four-node WDM ring with recirculation of blocked traffic.
Notation of traffic flow intensities
previous node through the counter-clockwise fibre (dashed
fibre link). Such blocked and redirected traffic, when arriving
at the previous (upstream) node can be treated following one
of two different policies, as illustrated in Fig. 2a, b:
• Recirculation bypass (Fig. 2a): In this case, recirculated
traffic has got priority over local traffic and it bypasses
the previous node directly to the blocked node without
any OEO conversion. In case there is local traffic waiting
for transmission, this must wait.
• Recirculation store-and-forward (Fig. 2b): In this case,
recirculated traffic is converted to the electronic domain
and must wait in queue together with local traffic. No
priority is given to recirculated traffic.
Fig. 2 Recirculation bypass
(left) and store and forward
(right). a Recirculation Bypass
b Recirculation
store-and-forward
123
Let N + 1 refer to the number of nodes in the ring of Fig. 1,
and let n i , i = 0, . . . , N be used to label each node in the
optical ring. Without loss of generality, the aim is to study
the delay experienced by the packets injected by any source
node n i with i = 1, . . . , N to the destination node n 0 , both
under the recirculation bypass and the recirculation storeand-forward policies. The following blocking analysis holds
for both policies.
3.1 Blocking analysis
As previously stated, each node is provided with a dedicated
home channel for reception, in this case, node n 0 continuously listens on wavelength λ0 . Thus, upstream nodes must
compete for accessing λ0 . Now, let ρi refer to the traffic load
that node n i offers to wavelength λ0 (that is, destined to node
n 0 ). In addition to this, ρi,o f f refers to the total amount of
traffic offered on segment i + , which basically comprises a
sum of traffic load intensities. Owing to the flow conservation
law on each node, the sum of incoming flow intensities must
equal the sum of outgoing flow intensities. This translates to
the following set of N + 1 equations:
Photon Netw Commun (2011) 21:278–287
281
ρout + ρ1,o f f B0 = ρ1,o f f
⇒ ρout = ρ1,o f f (1 − B0 )
ρ1,o f f + ρ2,o f f B1 = ρ1 + ρ2,o f f + ρ1,o f f B0
⇒ ρ1,o f f (1 − B0 ) = ρ1 + ρ2,o f f (1 − B1 )
ρ2,o f f + ρ3,o f f B2 = ρ2 + ρ3,o f f + ρ2,o f f B1
⇒ ρ2,o f f (1 − B1 ) = ρ2 + ρ3,o f f (1 − B2 )
.. .. ..
. . .
ρ N ,o f f = ρ N + ρ N ,o f f B N −1
⇒ ρ N ,o f f (1 − B N −1 ) = ρ N
where ρi+1,o f f Bi refers to the amount of traffic offered to
node i and blocked at this node (with probability Bi ).
It can be easily shown from the equations above that:
ρout = ρ1,o f f (1 − B0 ) = ρ1 + ρ2,o f f (1 − B1 )
= ρ1 + ρ2 + ρ3,o f f (1 − B2 ) = . . .
= ρ1 + ρ2 + · · · + ρ N ,o f f (1 − B N −1 )
=
N
(1)
ρi
i=1
which confirms that no data is lost (flow conservation law),
that is, all traffic injected in the network eventually arrives at
node n 0 .
N
ρi , the values of the offered trafGiven that ρout = i=1
fic ρi,o f f on each node are derived as:
ρ1,o f f =
N
1
ρout
=
ρi
1 − B0
1 − B0
E B (ρ, M) =
ρM
M!
M ρ j
j=0 j!
(4)
Thus, using Eq. 2 for ρi,o f f , the above Eq. 3 yields:
Bi−1 N
ρi + 1−B
k=i ρk
i−1
, i = 1, . . . , N
Bi =
Bi−1
N
1 + ρi + 1−B
k=i ρk
i−1
(5)
with B0 = 0 since the destination node is never blocked
because it never injects traffic on λ0 .
Thus, given a set of traffic intensities ρi destined to node
n 0 , it is very easy to compute the blocking probabilities Bi
from Eq. 5 recursively, that is: starting from B0 = 0, then
B0 N
B1 = ρ1 + 1−B
i=1 ρi = ρ1 , and so on. The next step
0
is to derive the amount of time required by each packet to
successfully arrive at the destination node following the two
recirculation policies: (1) store and forward and (2) bypass.
3.2 Delay analysis
i=1
ρ2,o f f =
N
ρ1,o f f (1 − B0 ) − ρ1
1
=
ρi
1 − B1
1 − B1
3.2.1 Recirculation store-and-forward
i=2
ρ3,o f f
ρ2,o f f (1 − B1 ) − ρ2
1
=
=
1 − B2
1 − B2
N
ρi
i=3
.. .. ..
. . .
ρ N −1,o f f (1 − B N −2 ) − ρ N −1
1
=
ρN
ρ N ,o f f =
1 − B N −1
1 − B N −1
So, in general, for node n i :
ρi,o f f =
N
1
ρk , i = 1, . . . , N
1 − Bi−1
(2)
k=i
This information is very useful for computing the blocking probabilities Bi experienced by transit traffic on each
node n i , using the well-known Erlang-loss equations. Essentially, the blocking probability experienced by transit traffic
on every node follows:
Bi = E B (ρi + ρi,o f f Bi−1 , 1), i = 1, . . . , N
(3)
where E B (ρ, M) refers to the Erlang-B loss equation of ρ
units of traffic to be served by M circuits. Remark that:
In this case, data frames arriving at a blocked node need
to travel back to the previous node in the ring, where they
suffer OE conversion and wait in queue together with the
node’s traffic load. Thus, assuming infinite buffer queues, no
buffer overflow occurs and all data frames eventually arrive at
their destination. However, data frames may need to recirculate several times certain segments if these are usually found
blocked, with subsequent unbounded delay. Thus, it is important to study both the delay mean and its variance to give an
idea of not only the average delay experienced on the ring
but also the jitter.
Under the assumption of unlimited electronic buffering,
the results of queueing theory for M/M/1 systems apply to
derive the average delay experienced at each node’s queue,
namely E(Q i ), i = 1, . . . , N . This value is given by:
E(Q i ) =
E(S)
1 − ρi
(6)
where E(S) is the average service time of a data frame of size
E(B) bits transmitted over a link of capacity C bits/s. In other
words: E(S) = E(B)/C. For a typical 1500-byte data frame
over a 10-Gbps link, this is, E(S) = 1500 · 8/1010 = 1.2 µs.
123
282
Photon Netw Commun (2011) 21:278–287
Now, let loop j refer to the segments j + and j − . Thus, a
given packet originated at node nl and destined to node n 0
experiences the following delay:
Dl = Q l + Reo +
l
L j + Roe
(7)
j=1
which accounts for the queueing delay experienced until it
is injected on the ring plus the amount of time L j spent on
each intermediate loop j, with j = 0, . . . , l − 1. Additionally, the EO and OE conversion delays (Reo and Roe in Eq. 2)
suffered when entering and exiting the ring respectively are
also considered in the model.
Now, consider loop j only: If the packet finds node n j
free (which occurs with probability 1 − B j ), then the packet
only suffers propagation delay R j . Otherwise, this packet
is reflected back to node n j+1 , converted to electronic, and
stored in the queue of node j +1 (this occurs with probability
B j ). In the next attempt, if the packet finds node n j free, then
the packet has experienced a total delay of 2R j + Q j+1 + R j
(this is with probability B j (1 − B j )). If the packet is successfully transmitted on the third attempt (with probability
B 2j (1 − B j ), then such packet experiences a total delay of
4R j + 2Q j+1 + R j , and so on. Following this reasoning,
the total delay experienced by a packet traversing loop j is
given by:
m
2R j + Roe + Q j+1 + Reo
L j = Rj +
the OE and EO conversion which are fixed quantities, i.e.
E(Roe ) = Roe and E(Roe ) = Roe . The loop’s delay variance V ar (L j ) is given by1 :
V ar (L j ) = V ar (R j )
+E(m)V ar (2R j + Roe + Q j+1 + Reo )
+(E(2R j + Roe + Q j+1 + Reo ))2 V ar (m)
Bj
Bj
V ar (Q j+1 ) +
=
1 − Bj
(1 − B j )2
2
× 2R j + Roe + E(Q j+1 ) + Reo
(11)
where V ar (R j ) = 0 since the propagation delay is a
fixed value. The same reasoning applies to V ar (Roe ) =
2
E(S)
.
V ar (Reo ) = 0. Additionally, V ar (Q j+1 ) = 1−ρ
j
Finally, the end-to-end delay experienced by a packet originated at node nl has got the following mean and variance:
l−1
1+B j
E(S)
Rj
+Reo +
E(Dl ) =
1−ρl
1−B j
j=0
Bj
+ Roe
+(Reo +E(Q j+1 )+Roe )
1−B j
l−1
Bj
E(S) 2
V ar (Dl ) =
+
V ar (Q j+1 )
1−ρl
1−B j
j=0
+
(8)
Bj
(1−B j )2
k=0
2
2R j +Reo +E(Q j+1 )+Roe
where m is a geometrically distributed random variable with
parameter B j . Essentially, m gives the number of extra
attempts required for the successful transmission of a given
packet over loop j, characterised by the probability B j to
find the next node n j blocked in the end-to-end path. In other
words:
3.2.2 Recirculation bypass
P(m = k) = (1 − B j )B kj , k = 0, 1, . . .
In this case, the same Eq. 2 as above applies here:
(9)
Additionally, it is worth remarking from Eq. 8 that packets must suffer OE and EO delay whenever they find the next
node blocked, since they must be electronically buffered on
the immediate upstream node.
The mean delay for loop L j is given by:
E(L j ) = E(R j )+E(m)E(2R j +Roe +Q j+1 +Reo )
Bj
2E(R j )+E(Roe )+E(Q j+1 )
= E(R j )+
1 − Bj
+ E(Reo ))
Bj
1+B j
= Rj
+(Roe +E(Q j+1 )+Reo )
(10)
1 − Bj
1 − Bj
where E(R j ) = R j since the propagation delay is a fixed
value given by the fibre length and the speed of light on
the optical fibre (typically 2 · 108 m/s). The same applies to
123
(12)
(13)
under the assumption of node independency.
As shown, at low load levels, a given packet originated at
node l would ideally experience a delay of E(Q l )+ l−1
j=0 R j .
Dl = Q l + Reo +
l
L j + Roe
(14)
j=1
However, the computation of Q l and L j is rather different.
First of all, the delay experienced on the j-th loop, L j , does
not include queueing delay since, recirculated traffic does not
suffer OEO conversion and queueing on the previous nodes.
Thus:
L j = Rj +
m
2R j
(15)
k=0
1 Remark that the variance of a random sum of N iid random variN
X i ) = E(N )V ar (X 1 ) +
ables X i , i = 1, 2, . . . is given by: V ar ( i=1
2
E (X 1 )V ar (N ).
Photon Netw Commun (2011) 21:278–287
283
In addition, the average queueing delay experienced by the
packets before entering the ring is also different from the
previous case:
E(Q i ) =
E(S)
(1 − ρi )(1 − Bi−1 )
(16)
Since the capacity observed by the queue on node n i is
only the remaining one left by the recirculated traffic, that is,
C(1 − Bi−1 ).
Thus, the mean delay and variance experienced by packets
on loop L j are given by:
E(L j ) = E(R j ) + E(m)E(2R j )
Bj
1 + Bj
2E(R j ) = R j
= E(R j ) +
1 − Bj
1 − Bj
1 µs
= 1.0526 µs
1 − 0.05
60/8 km
= 37.5 µs
2 · 105 km/s
(17)
R=
(18)
Clearly, the total delay depends on the number of segments
that a given packet must traverse until reaching its destination
(its relative position in the ring) and the number of times that
such a packet must recirculate each segment (which depends
on the blocking probabilities) before reaching their destination. Additionally, the values of Roe and Reo may also
comprise a significant portion of it.
The next section explores such average delay and its variance on different topologies and under uniform and nonuniform traffic loads.
V ar (L j ) = V ar (R j ) + E(m)V ar (2R j )
where V ar (R j ) = 0 since the propagation delay is a fixed
2
E(S)
.
value. Additionally, V ar (Q j+1 ) = 1−ρ
j
Finally, the end-to-end delay mean and variance for packets under the recirculation bypass strategy is given by:
E(S)
+ Reo
(1 − ρl )(1 − Bl−1 )
l−1
1 + Bj
+ Roe
Rj
+
1 − Bj
j=0
2
E(S)
V ar (Dl ) =
(1 − ρl )(1 − Bl−1 )
l−1
Bj
2
4
+
R
(1 − B j )2 j
E(Q) =
and suffer the following propagation delay per segment:
and
+(E(2R j ))2 V ar (m)
Bj
=
(2R j )2
(1 − B j )2
where ρ denotes the input queue load. Finally, both OE and
EO delays have been assumed Roe = Reo = 25 µs.
To give an example with real numbers in the recirculation store-and-forward policy, let the ring comprise N + 1 =
8 nodes equally spaced on a 60 km long ring. Also, let all
nodes operate under the same traffic load ρ = 0.05, then the
queueing delay experienced by a packet to enter the ring is
given by:
4.1 Analysis validation via simulation
E(Dl ) =
(19)
(20)
j=0
again under the assumption of node independency.
4 Numerical examples
This section aims to validate the analytical equations derived
above and perform a few simulation scenarios to determine
what aspects have a greater impact on delay and jitter in the
ring. The scenario considers a 60- km ring with N + 1 nodes
labelled n 0 to n N with node n 0 acting as destination node. The
size of packets injected in the ring is exponentially-distributed with mean E(B) = 1250 bytes, thus giving an average
= 1 µs on a C = 10 Gbps
service time: E(S) = 1250×8
10·109
interface. Additionally, nodes are assumed to aggregate traffic from multiple users, leading to traffic profile injected in
the ring that follows a Poisson process with rate λ = ρ/E(S),
This first experiment validates the delay equations derived
through the analysis section with simulation. The simulation was developed in Matlab’s Simulink for a 60- km ring
with N + 1 = 8 nodes at different input loads, and assuming the values of capacity C = 10 Gbps, E(B) = 1250
bytes and Roe = Reo = 25 µs, as described above. It is also
worth remarking that the maximum input load per node is
ρmax = 1/(N + 1), since the maximum offered load on the
last segment must not exceed unity.
Figure 3 shows both the analytical and simulated results
for such a ring, assuming both policies upon blocked traffic: Recirculation store-and-forward (top) and recirculation
bypass (bottom). For brevity purposes, only the delay experienced by the first and the last nodes in the ring, together with
the node in the middle, are depicted. As noted, both analytical and simulated values accurately match one another both
in terms of delay mean (dots) and standard deviation (error
bars), at different traffic loads. The reader must note that the
error bars represent the standard deviation of delay (not confidence intervals) in units of time. In this case, the maximum
input load per node is ρmax = 1/(N + 1) = 0.125.
The next experiments consider only the analytical results
to show the benefits and shortcomings of the two policies
(Recirculation bypass and store-and-forward) on different
scenarios.
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284
Photon Netw Commun (2011) 21:278–287
N=8, Recirculation Store−and−Forward
N=8, Recirculation Store−and−Forward Simulated
700
E2E delay (µs)
E2E delay (µs)
700
600
500
400
300
200
100
0
0
600
500
400
300
200
100
0.02
0.04
0.06
0.08
0.1
0
0
0.12
0.02
0.04
Load ρ
400
400
300
200
100
0.04
0.06
0.1
0.12
N=8, Recirculation Bypass Simulated
500
E2E delay (µs)
E2E delay (µs)
N=8, Recirculation Bypass
0.02
0.08
Load ρ
500
0
0
0.06
0.08
0.1
300
200
100
0
0
0.12
0.02
Load ρ
0.04
0.06
0.08
0.1
0.12
Load ρ
Last node
Half−distant node
First node
Fig. 3 Analysis validation with Matlab’s Simulink for a network with N = 8 nodes. Analytical results (on the left) and Simulation results (on the
right) are obtained assuming recirculation Store-and-Forward (top) and recirculation bypass (bottom)
4.2 Delay analysis for different values of N
This experiment provides a comparison between the two policies when the number of nodes in the ring varies. Remark
that the ring length is 60- km fixed and the values for E(B) =
1250 bytes, C = 10 Gbps and Roe = Reo = 25 µs are the
same as before. Two cases are considered: (a) N + 1 = 8 and
(b) N + 1 = 32. In the first case, the propagation delay per
3 /8
= 37.5 µs whereas in the second
segment is R = 60·10
2·108
3
/32
= 9.37 µs. The average delay and
case this is R = 60·10
2·108
variance is given in Fig. 4 for the two cases at different link
loads. Again for brevity, only the first, last and a node in the
middle of the ring are plotted.
As shown in the figure, there is a great performance difference (in terms of delay mean and variance) between the
recirculation bypass and the recirculation store-and-forward
policies, in both cases, especially at high loads. In all cases,
the recirculation bypass policy for blocked frames is shown
to reduce the average delay experienced by packets and its
variance since these do not suffer OEO conversion. Additionally we can note the following conclusions:
• The first node does not experience a big difference in
terms of delay mean and variance in all cases. This is
because the closest nodes perceive a high-priority treat-
123
ment with respect to last nodes, thus experiencing only
about R + Roe + Reo in most cases.
• At low loads, there is no big difference between the average delay experienced by packets in the two policies, but
there is when it comes to variance (jitter).
• When the recirculation bypass technique is used, there
is no big difference in terms of average delay between a
60- km ring with 8 or 32 nodes, but there is in terms of
variance. This is an important conclusion to keep in mind
when upgrading a fixed-length ring with more intermediate nodes.
• The opposite conclusion occurs in the recirculation storeand-forward technique since it is shown that there is not a
big difference in terms of variance when upgrading from
8 to 32 nodes, but there is some difference in terms of
average delay.
4.3 Delay analysis when one node offers a peak of traffic
Figure 5 shows the delay mean and variance observed on each
node in the ring assuming that a given node abuses from the
network resources. In this experiment, all nodes are assumed
lightly loaded (ρ = 0.0312) except a misbehaving one which
transmits an amount of traffic equal to ρpeak = 0.75. As
shown, when this occurs, the effect observed is that this misbehaving node blocks access to the previous ones in the ring,
Photon Netw Commun (2011) 21:278–287
285
N=8, Recirculation bypass
600
500
500
E2E delay (µs)
E2E delay (µs)
N=8, Recirculation Store−and−Forward
600
400
300
200
100
0
0
0.02
0.04
0.06
0.08
0.1
400
300
200
100
0
0
0.12
0.02
0.04
Load ρ
500
500
400
300
200
100
0.005
0.01
0.015
0.08
0.1
0.12
N=32, Recirculation bypass
600
E2E delay (µs)
E2E delay (µs)
N=32, Recirculation Store−and−Forward
600
0
0
0.06
Load ρ
0.02
0.025
400
300
200
100
0
0
0.03
0.005
0.01
Load ρ
0.015
0.02
0.025
0.03
Load ρ
Half−distant node
Last node
First node
Fig. 4 Delay mean and variance experienced by packets in the two policies for variable number of nodes N + 1
Peak on node 1
Peak on node 1
700
700
Recirculation Store−and−Forward
Recirculation bypass
600
E2E delay (µs)
E2E delay (µs)
600
500
400
300
200
100
0
0
500
400
300
200
100
1
2
3
4
5
6
0
0
7
1
2
Node index
Peak on node 5
5
6
7
5
6
7
700
Recirculation Store−and−Forward
Recirculation bypass
600
E2E delay (µs)
600
E2E delay (µs)
4
Peak on node 5
700
500
400
300
200
100
0
0
3
Node index
500
400
300
200
100
1
2
3
4
5
6
7
Node index
0
0
1
2
3
4
Node index
Fig. 5 Delay mean and variance on each node assuming a peak of traffic on nodes n 1 (top) and on node n 6 (bottom) on an 8-node WDM ring
thus increasing very significantly their delay mean and especially their variance. This is particularly harmful in the recirculation store-and-forward case, where the nodes before the
misbehaving one experience a significant increase in their
delay and variance due to multiple OEO conversions and
queueing. When employing recirculation bypass, node abuse
is specially harmful in terms of delay variance, rather than
by means of delay mean.
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286
5 Conclusions
This work has proposed a novel MAC protocol to avoid channel collisions in TT-FR-based WDM rings. The novelty introduced by this MAC protocol is that blocked traffic is recirculated back to upstream nodes, where they can be directly
forwarded to the next node (Recirculation bypass) or stored
in queue and be forwarded next (Recirculation store-andforward). In both cases, the delay mean and variance experienced by the packets are analysed to show the difference in
terms of performance in both cases. The experiments reveal
that the recirculation store-and-forward introduces more delay to packets than recirculation bypass, especially at high
traffic loads and, more significantly, a tremendous delay variance, which is very harmful for real-time traffic. Such a
model can be used to further study the impact of both policies on traffic demanding strict QoS requirements.
Acknowledgments The work described in this paper was carried out
with the support of the BONE project (“Building the Future Optical
Network in Europe”), a Network of Excellence funded by the European
Commission through the 7th ICT-Framework Programme. Additionally, the authors would like to thank the support of the T2C2 Spanish
project (under code TIN2008-06739-C04-01) to the development of
this work.
References
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Author Biographies
Isaac Seoane received the Telecommunications Engineering degree in 2004 and the
M.Sc. in Telematics Engineering in 2007 at
Universidad Carlos III de Madrid (Spain).
He is an assistant lecturer and researcher at
the Department of Telematic Engineering at
Universidad Carlos III de Madrid (Spain)
since 2006 where he has participated in several national and European researching projects, such as IMPROVISA, T2C2, and the EU-funded e-Photon/ONe+,
BONE and Indect. He is currently working on his Ph.D. Thesis about
optical ring networks and also doing research in some other networking-related topics such as emergency networks, multipath and multiple
description for multimedia content.
Gerson Rodríguez de los Santos received
his Telecommunications Engineering degree
in April 2008 and is pursuing the M.Sc.
in Telematics Engineering at Universidad
Carlos III de Madrid (Spain). He is currently working at Universidad Carlos III as a
research assistant, providing technical support for a number of both national and european research projects (INDECT, BONE,
PASITO, T2C2, etc). His research interests cover the fields of Optical
Transparent Networks, Network Hardware development and Switching
in general. He is also pursuing the Ph.D. degree in Telematic Engineering at the aforementioned University.
José Alberto Hernández completed the
five-year degree in Telecommunications
Engineering at Universidad Carlos III de
Madrid (Madrid, Spain) in 2002, and the
Ph.D. degree in Computer Science at Loughborough University (Leics, United Kingdom)
in 2005. From 2005 to 2009, he was a postdoctoral research and teaching assistant at
Universidad Autónoma de Madrid, where he
participated in a number of both national and european research projects
concerning the modeling and performance evaluation of communication networks, and particularly the optical burst switching technology.
In 2009, he moved to Universidad Carlos III de Madrid, where he currently works as a visiting lecturer and senior researcher, with more than
40 articles published in both journals and conference in-proceedings.
His research interests include the areas at which mathematical modeling and computer networks overlap.
Manuel Urueña received the M.Sc. degree
in Computer Science in 2001 from Universidad Politécnica de Madrid and the Ph.D. in
Telecommunications in 2005 from Universidad Carlos III de Madrid. At present, he is
an assistant professor of Telematics engineering at Universidad Carlos III de Madrid. His
research activities range from P2P systems,
through load balancing and service discovery
protocols, to Optical networks. He has been involved in international
and national research projects related with these topics, including the
EU IST GCAP and the EU SEC INDECT projects.
Photon Netw Commun (2011) 21:278–287
Ricardo Romeral obtained his M.Sc. degree in Telecommunications Engineering and
his Ph.D. in Telemeatics Engineering from
Universidad Carlos III de Madrid (Spain) in
2001 and 2007 respectively. Dr. Romeral is
an assistant professor at Universidad Carlos
III de Madrid since then, where he combines
lecturing and research in the fields of network
measuring and monitoring, GMPLS and optical networks, among many others. He has collaborated in several European and Spanish projects related to traffic monitoring and analysis in
optical backbone networks, and programmable networking.
Ángel Cuevas received his M.Sc. in Telecommunication Engineering and M.Sc. in
Telematic Engineering at Universidad Carlos
III de Madrid in 2006 and 2007, respectively.
He was awarded with an Erasmus Scholarship and complete his Master Thesis at
The University of Reading. Currently he is
Ph.D. Candidate at the Department of Telematic Engineering at University Carlos III de
Madrid. Also, he held a research Internship at SAP Labs France. His
research interests include Wireless Sensor Networks, Overlay and P2P
Networks and Optical Networks.
287
David Larrabeiti [M’96] is currently a full
professor at Universidad Carlos III de Madrid
(Spain) since 1998, where he teaches several modules concerning high-speed switching networks and architectures. He received
the M.Sc. and Ph.D. degrees in Telecommunications Engineering from Universidad
Politécnica de Madrid in 1991 and 1996
respectively. He has participated in a large
number of both national and international research projects focused on
next-generation networks for more than a decade. His research interests
include the design of the future Internet infrastructure, ultra-broadband
multimedia transport, and traffic engineering over IP-GMPLS backbones. His email address is dlarra@it.uc3m.es.
123