Computational complexity of loss networks
Theoretical Computer Science - Special issue on probabilistic modelling
Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects
Manufacturing & Service Operations Management
Stability of the bipartite matching model
ACM SIGMETRICS Performance Evaluation Review
A reversible erlang loss system with multitype customers and multitype servers
Probability in the Engineering and Informational Sciences
A product form solution to a system with multi-type jobs and multi-type servers
Queueing Systems: Theory and Applications
A product form solution to a system with multi-type jobs and multi-type servers
Queueing Systems: Theory and Applications
Queues with skill based parallel servers and a FCFS infinite matching model
ACM SIGMETRICS Performance Evaluation Review
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Motivated by queues with multitype servers and multitype customers, we consider an infinite sequence of items of types C = {c1,...,cI}, and another infinite sequence of items of types S = {s1,...,sJ}, and a bipartite graph G of allowable matches between the types. We assume that the types of items in the two sequences are independent and identically distributed (i.i.d.) with given probability vectors α, β. Matching the two sequences on a first-come, first-served basis defines a unique infinite matching between the sequences. For (ci,sj) ∈ G we define the matching rate rci, sj as the long-term fraction of (ci, sj) matches in the infinite matching, if it exists. We describe this system by a multidimensional countable Markov chain, obtain conditions for ergodicity, and derive its stationary distribution, which is, most surprisingly, of product form. We show that if the chain is ergodic, then the matching rates exist almost surely, and we give a closed-form formula to calculate them. We point out the connection of this model to some queueing models.