We consider a memoryless single station service system with servers S=₁,…,mK\ , and with job types C=,b,…\ . Service is skill-based, so that server m i 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.
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Visschers et al. (2012) studied this question.