Structural properties and stochastic bounds for a buffer problem in packetized voice transmission

Abstract

We consider a communication channel which carries packetized voice. A fixed number (K) of calls are being transmitted. Each of these calls generates one packet at everyC timeslots and the channel can transmit at most one packet every timeslot. We consider the nontrivial caseK ≤C. We study the effectsK, C and the arrival process have on the number of packets in the buffer.

When the call origination epochs in the firstC timeslots of theK calls are uniformly distributed (i.e. when the arrivals during the firstC timeslots have a multinomial distribution) it is shown that the stationary number of calls waiting in the buffer is stochastically increasing and convex in the number of calls. For a fixed average number of calls per slot, it is shown that increasing the number of slots per frame increases the stationary number of packets in the buffer in the sense of increasing convex ordering. Using this, it is shown that the stationary number of packets in the buffer is bounded from above by the number of packets in a stationary discreteM/D/1 queue with arrival rateK/C and unit service time. This bound is in the sense of the increasing convex order.