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IX. PERFORMANCREE SULTS Both performance measures discussed in this paper, namely data-packet delay and voice-call blocking probability, have been evaluated computationally. In this section we present the results of our evaluation of both fixed- and movable-boundary versions of the WIMA protocol. All of the results are for M = MV = 10 and L = R = 12. Our earlier studies of the IFF0 protocols have shown that performance is quite insensitive to the number of terminals for M greater than about 5 [3], and this behavior has also been observed for the WIMA protocol; thus the results for M = 10 are representative of higher values as well. The number of iterations required for convergence ranged from 2 at extremely low throughput rates to more than 2000 at extremely high throughput rates. Fig. 6 shows the expected data-packet system time (which is normalized with respect to the frame length L) as a function of data throughput for the fixed-boundary WIMA scheme for values of V, ranging from 0 to 6. Note that data throughput is defined to be the expected number of data packets successfully delivered by the system per time slot,where the average is taken over all L slots in the frame, including the status slot and those that are used for voice transmission. Recall that this performance index is independent of all voice-call parameters except V, in fixed-boundary systems. Note that the curve for V, = 0 is actually the curve for PR-NIFFL, which is data-only system. The maximum achievable data throughput under the WIMA schemes is (L - 1 - Vmax)/L, and we may define the "utilization" to be the data throughput normalized by this quantity. As the utilization approaches 1, which occurs at different values of data throughput for different values of V, the expected delay increases to co. For all values of V, results were obtained for utilization values of at least 0.98 (for which a 700 x 700 transition matrix was used), thereby demonstrating the ability of our model to evaluate heavily-loaded systems. Fig. 7 shows the effect of varying pv (and hence the expected length of voice calls) over a wide range for the movable-boundary scheme with V,,, = 6, while Xv is kept fixed at 0.01. For small values of pv, the system is heavily loaded, and performance approaches that of the fixed-boundary scheme. As pv increases, the average length of voice calls decreases, resulting in a decrease in the voice-call load and hence an increase in the number of slots available for data traffic. Thus the system is able to support higher levels of data traffic. Fig. 8 shows the voice-call blocking probability as a function of Vmax for Xv = 0.01 and several values of pv. Clearly,increasing Vmax results in lower blocking probability because more of the channel resource is available for the voice calls. Also, since large values of pv correspond to short voice calls,increasing pv results in lower channel utilization and hence in lower blocking probability. |
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