Approximations for Multi-Class Departure Processes

The exact analysis of a network of queues with multiple products is, in general, prohibited because of the non-renewal structure of the arrival and departure processes. Two-moment approximations (decomposition methods, Whitt [9]) have been successfully used to study these systems. The performance of these methods, however, strongly depends on the quality of the approximations used to compute the squared coefficient variation (CV) of the different streams of products. In this paper, an approximation method for computing the squared coefficient of variation of the departure stream from a multi-class queueing system is presented. In particular, we generalize the results of Bitran and Tirupati [3] and Whitt [11] related to the interference effect. A single server queueing station serves, according to a FIFO policy, a family of n different products. The arrival process of product i (i = 1,. .. , n) is renewal and it is characterized by the counting process {N i (t): t 0}. The arrival processes are independent across products. In addition, we define • X i : the random variable that describes the inter-arrival interval for product i. • λ i = (E[X i ]) −1 : the mean arrival rate of product i.