A product form solution to a system with multi-type jobs and multi-type servers
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(i) 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.
product form solution multi-type jobs multi-type servers service system first-come-first-served policy partial balance