A product form solution to a system with multi-type jobs and multi-type servers

Abstract

We consider a memoryless single station service system with servers S = {m1,...,mK}and with job types C = {a,b...}. Service is skill-based, so that server mi can serve a subset of job types C(mi). Waiting jobs are served on a first-come-first-served basis, while arriving jobs that find several idle servers are assigned to a feasible server randomly. We show that there exist assignment probabilities under which the system has a product-form stationary distribution, and obtain explicit expressions for it. We also derive waiting time distributions in steady state. © 2012 The Author(s).