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

摘要

We consider a memoryless single station service system with servers S = {m 1,..., m K}, and with job types C = {a,b,...}. Service is skill-based, so that server m, can serve a subset of job types C(m i). 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.