An entropy measure of operating performance uncertainty in queues: Markovian examples

In information theory, Shannon (1948), entropy function is used to measure message uncertainty and communication channel capacity. Shannon entropy considers the probability distribution of signals transmitted over a given communication channel in its argument of uncertainty. Since the concept of the steady-state of a queue (assuming it obtains) concerns a probability function, it seems logical to consider a connection between entropy and the uncertainty in queueing. Hence, using information-theoretic entropy, and the notions of steady-state (SS), and steady-state distribution (SSD), this paper presents an entropy-based uncertainty metric for measuring the operating performance of (Markovian) queues. M/M1 and M/M/1/k models are used as examples. The proposed method offers the practical value of establishing how good (i.e., dependable) the long-run results for a queue are. This could be valuable for decision-making purposes, especially when alternative models may be available to choose from. A model choice, which has less uncertainty, should be more desirable than one that exhibits high uncertainty, since the latter would experience a more chaotic, more disorderly steady-state and long-run operating behaviour.