The multiserver station with dynamic concurrency constraints

Abstract

This paper defines the the Multiserver Station With Dynamic Concurrency Constraints. The MSDCC station consists of B parallel identical exponential servers. The customers requesting service at the MSDCC station belong to C types. Customers arriving at the MSDCC station are queued for service in FCFS order. A set of tokens (B1 • • • Bc) is associated with the MSDCC station where Bc is the number of type c tokens. The tokens are used to enforce a system of dynamic concurrency constraints which limits the number of customers of each type that may simultaneously be in service. The concurrency constraints operate as follows. A type c customer may only enter into service if a server is free and a type c token is available. When entering into service a type c customer seizes a type c token. The token is retained while the customer is in service. Upon completing service the customer releases the type c token which, according to a Bernoulli trial, changes into a type d token. This paper defines the MSDCC station and proves that the MSDCC station has a product form solution. Several examples of state dependent token switching functions are given. Finally, an efficient recursive expression is derived for the queue length distribution at the MSDCC station.