A Queueing Loss Model with Heterogeneous Skill Based Servers Under Idle Time Ordering Policies. (30th January 2018)

• Record Type: Journal Article
• Authors: Haji, Babak; Ross, Sheldon M.
• Is Part Of: Journal of applied probability. Volume 52:Number 1(2015)
• Page Start: 269
• Page End: 277
• Publication Date: 2018-01-30
• Subjects: Heterogeneous server, -- queueing loss system, -- limiting probability, -- no-memory policy, -- method of stages, -- reverse chain, -- equilibrium distribution, -- Gibbs sampler; 60K25, -- 60J27, -- 90B22; 519.2
• DOI: 10.1239/jap/1429282621
• Languages: English
• ISSNs: 0021-9002

Abstract

Abstract : We consider a queueing loss system with heterogeneous skill based servers with arbitrary service distributions. We assume Poisson arrivals, with each arrival having a vector indicating which of the servers are eligible to serve it. An arrival can only be assigned to a server that is both idle and eligible. Assuming exchangeable eligibility vectors and an idle time ordering assignment policy, the limiting distribution of the system is derived. It is shown that the limiting probabilities of the set of idle servers depend on the service time distributions only through their means. Moreover, conditional on the set of idle servers, the remaining service times of the busy servers are independent and have their respective equilibrium service distributions.