K ar akt er ist ik Sist em A nt r ian
6.2 K ar akt er ist ik Sist em A nt r ian
² Beberapa key element s: cust omers, servers dan net work of queues
Calling p opulat ion: The populat ion of pot ent ial cust omers is refered t o as t he calling popu-
lat ion. Use examples fr om Table 7.1 ² The calling populat ion can be …nit e or in…nit e.
² I n t he syst ems wit h large populat ion, we usually assume t he populat ion is in…nit e.
² The key di¤erence bet ween “ …nit e” and “ in… nit e” populat ion model is how t he arr ival rat e is de…ned.
– In an in…nit e populat ion model, t he arrival rat e is not a¤ect ed by t he number of cust omer s in t he syst em. Usually t he syst em is viewed as an open syst em, cust omers come from out side t he syst em and leave t he syst em aft er … nishing t he work.
– In a …nit e populat ion model, t he arrival rat e at a server is a¤ect ed by t he populat ion in t he syst em. Usually t he syst em is viewed as
a closed syst em, cust omers (wit h a …xed populat ion) don’t leave t he syst em, t hey merely move around syst em from one server t o anot her , from one queue o anot her.
Syst em capacit y: t he maximum number of cust omers allowed in t he syst em is called t he
syst em capacit y. Examples: ² Telephone boot h: capacity is one. When t he server is busy (t he boot h
occupied), t he incoming cust omer is t urned away. ² A t ypical T CP/ I P packet bu¤er has a limit of 4096 byt es. ² The number of simult aneous connect ions allowed at a web server usu-
ally is a … xed const ant . T he ar r ival pr ocess:
for in…nit e population
– scheduled arr ivals, such as pat ient s t o a physician’s o¢ ce; airline ‡ight arr ives at an airport . The int erarrival t ime may be a con- st ant , or a const ant wit h a small random ‡uct uat ion.
– at least onecust omer is assumed t o always be present in t hequeue, so t he server is never idle because of t he lack of t he cust omers,
e.g. part s in an assembly line. for …nite population: – De…ne a cust omer is pending when it is out side queueing syst em,
and it is a member of t he pot ent ial calling populat ion. E.g. when simulat ing a local area net work, if a part icular comput er is pow- er ed o¤, we say it is pending. As soon as it is powered on, t he cust omer (comput er) will demand service from t he net work.
– De…ne runt ime of a given cust omer as t he lengt h of t he t ime from depart ure from t he queueing syst em unt il t he cust omer’s next ar- rival t o t he queue. Runt ime essent ially is t he t ime when t he cus- t omer is being ser viced.
The ar rival rat e in a … nit e populat ion model is a funct ion of t he number of pending cust omers.