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It is clear that the desire to minimize data-packet delay and to minimize voice-call blocking probability represent conoflicting goals. In such cases with two competing performance indexes, it is customary to attempt to minimize their weighted sum E(D) + ¦ÁP B .
Fig. 9 shows this weighted performance index as a function of Vmax for the fixed-boundary version and a = 2, where delay is again normalized with respect to R. The curves are plotted for a fixed value of data-packet throughput. Note that for throughput values of 0.48 and greater, the curves terminate at values of Vmax less than 6; in each of these cases the value of throughput corresponds to a utilization of 0.96 for the corresponding value of Vmax. Throughput values that
correspond (for a specific value of vmax) to a utilization of 1.0 or greater result in infinite delay, and hence an infinite value of the weighted performance index. The tradeoffs between the two performance indexes are apparent; as throughput decreases the optimal value of Vmax increases.
VIII. EVALUATION OF VOICE-CALL BLOCKINGP ROBABILITY
The performance measure used for voice traffic is the voice call blocking probability, which is denoted by PB. Whenever a slot is not available for a new call, the call is blocked and dropped from the system. Thus, PB depends only on Vmax and the voice-call arrival (XV) and completion (pv) probabilities, and is independent of the data-traffic parameters. We define
BI, = number of calls blocked in frame k.

The only remaining quantity needed to evaluate PB by using (8.1) is the expected number of voice arrivals  per frame. To determine this quantity we again make use of the fact that the arrival process is indpendent of the system state to obtain.

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