Entropy maximised queueing networks with blocking and multiple job classes

Abstract

The method of entropy maximisation (MEM) is applied in a state space partitioning mode for the approximation of the joint stationary queue length distribution of an M/M/1/N queue with finite capacity, N( > 1), multiple and distinct classes of jobs, R( > 1), under a complete buffer sharing scheme and mixed service disciplines drawn from the first-come-first-served (FCFS), last-come-first-served with (LCFS-PR) or without (LCFS-NPR) preemption and processor sharing (PS) rules. The marginal and aggregate maximum entropy (ME) queue length distributions and the associated blocking probabilities per class are also determined. These ME results in conjunction with the first moments of the effective flows are used, as building blocks, in order to establish a new product-form approximation for arbitrary exponential open queueing networks with multiple classes of jobs under repetitive-service (RS) blocking with random destination (RD). It is verified that the ME approximation reduces to the exact truncated solution of open multi-class reversible queueing networks. Numerical experiments demonstrate a good accuracy level of ME statistics in relation to simulation. Moreover, recent extentions of MEM for arbitrary GE-type queueing networks with RS-RD blocking and multiple classes of jobs are presented.