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A queueing analysis of a multichannel, integrated voice and data communications system Haller, Dennis Raymond


A multichannel radio communications system is modeled as a multiserver queue, with two distinct customer classes representing voice and data messages. Data, the class with the shorter average length, is given non-preemptive priority over voice. The queueing model is analyzed as a continuous-time Markov chain with an infinite state space. The infinite set of steady state balance equations is truncated, then solved numerically using the linear programming (LP) technique of Kotiah. Upper and lower bounds are thereby obtained for the mean waiting times of each customer class, and the probability distribution for the number of messages in the system. Exploitation of the Markov chain's property of irreducibility improves the original algorithm by considerably reducing the computational cost. Simulation is used to help analyze the system and to validate the numerical results. The particular four-channel case of the queueing model is treated in detail; both simulation and numerical results are presented. The LP method produces excellent results when the data traffic intensity is less than about 0.1. This corresponds typically to the proportion of data messages being less than 90%. For other traffic mixtures, the upper bounds, especially for waiting times, are often too high to be of practical use. However, the lower bounds of the mean waiting times are of greater use; the simulation results show them to be reasonably good approximations to the true steady state values.

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