Most-Urgent-Cell-First Algorithm MUCFA OUTPUT-QUEUING EMULATION

INPUT-BUFFERED SWITCHES 72 Ž . worst case arbitration delay to D s 4 g q 5d q 2 Nrn y 2 gates, where t u Ž .v d s log nrg . The hierarchical method basically decreases the time spent 2 in the group where the token is generated and in the group where the token is terminated. For N s 256, n s 16, and g s 2, the basic token tunneling method requires a 92-gate delay, whereas the hierarchical method requires only a 51-gate delay.

3.4 OUTPUT-QUEUING EMULATION

The major drawback of input queuing is that the queuing delay between inputs and outputs is variable, which makes delay control more difficult. Can an input᎐output-buffered switch with a certain speedup behave identically 4 to an output-queued switch? The answer is yes, with the help of a better scheduling scheme. This section first introduces some basic concepts and then highlights some scheduling schemes that achieve the goal.

3.4.1 Most-Urgent-Cell-First Algorithm MUCFA

w x The MUCFA scheme 29 schedules cells according to their urgency. A shadow switch with output queuing is considered in the definition of the Ž . urgency of a cell. The urgency, which is also called the time to leave TL , is the time after the present that the cell will depart from the output-queued Ž . OQ switch. This value is calculated when a cell arrives. Since the buffers of the OQ switch are FIFO, the urgency of a cell at any time equals the number of cells ahead of it in the output buffer at that time. It gets decremented after every time slot. Each output has a record of the urgency value of every cell destined for it. The algorithm is run as follows: 1. At the beginning of each phase, each output sends a request for the Ž . most urgent cell i.e., the one with the smallest TL to the correspond- ing input. 2. If an input receives more than one request, then it will grant to that output whose cell has the smallest urgency number. If there is a tie between two or more outputs, a supporting scheme is used. For example, the output with the smallest port number wins, or the winner is selected in a RR fashion. 3. Outputs that lose contention will send a request for their next most urgent cell. 4. The above steps run iteratively until no more matching is possible. Then cells are transferred, and MUCFA goes to the next phase. An example is shown in Figure 3.17. Each number represents a queued cell, and the number itself indicates the urgency of the cell. Each input Ž . maintains three VOQs, one for each output. Part a shows the initial state of 4 Under identical inputs, the departure time of every cell from both switches is identical. OUTPUT-QUEUING EMULATION 73 Fig. 3.17 An example of two phases of MUCFA. the first matching phase. Output 1 sends a request to input 1, since the HOL cell in VOQ is the most urgent for it. Output 2 sends a request to input 1, 1, 1 since the HOL cell in VOQ is the most urgent for it. Output 3 sends a 1, 2 request to input 3, since the HOL cell in VOQ is the most urgent for it. 3, 3 Ž . Part b illustrates matching results of the first phase, where cells from Ž . VOQ , VOQ , and VOQ are transferred. Part c shows the initial state 1, 1 2, 2 3, 3 Ž . of the second phase, while part d gives the matching results of the second phase, in which HOL cells from VOQ and VOQ are matched. 1, 2 3, 3 It has been shown that, under an internal speedup of 4, a switch with VOQ and MUCFA scheduling can behave identically to an OQ switch, regardless of the nature of the arrival traffic.

3.4.2 Chuang et al.’s Results