INSENSITIVITY AND PRODUCT-FORM DECOMPOSABILITY OF REALLOCATABLE GSMP

A stochastic process, called reallocatable GSMP (RGSMP for short), is introduced in order to study insensitivity of its stationary distribut ion. RGSMP extends GSMP with interruptions, and is applicable to a wid e range of queues, from the standard models such as BCMP and Kelly's n etwork queues to new ones such as their modifications with interruptio ns and Serfozo's (1989) non-product form network queues, and can be us ed to study their insensitivity in a unified way. We prove that RGSMP supplemented by the remaining lifetimes is product-form decomposable, i.e. its stationary distribution splits into independent components if and only if a version of the local balance equations hold, which impl ies insensitivity of the RGSMP scheme in a certain extended sense. Var ious examples of insensitive queues are given, which include new resul ts. Our proofs are based on the characterization of a stationary distr ibution for SCJP (self-clocking jump process) of Miyazawa (1991).