Approximate Analysis of a Cyclic Queuing Network with Applications to a Simultaneous Resource Possession Problem

Abstract In this paper we develop very accurate approximations for all mean performance measures of interest, for a class of cyclic queuing networks (CQNs). The number of nodes K, and the closed chain population N, are finite but arbitrary. Each node processes type t customers from the single closed chain, and type o customers from a dedicated open chain. The queuing discipline at each node is FIFO and the service time distribution for both type t and o customers is exponential, but with distinct service rates for each. Service rates may differ from node to node. Although the structure of this class of queuing networks is simple, very little is known in the literature except for the special case where the network reduces to a product form network. An analytic study of the approximation demonstrates that it mirrors the expected behavior of the CQN in many essential respects: monotonicity, bottleneck and asymptotic behavior. Moreover, in the case of balanced CQNs, the approximation yields simple and explicit expressions for all quantities of interest. This analytic study complements the numerical experiments presented and suggests that the approximation captures the essential structure of the CQN, insofar as mean performance quantities are concerned.