Queues with Skill Based Parallel Servers and a FCFS Infinite Matching Model

Abstract : We consider the following skill based parallel service queue-ing system: Customers are of types C = {c1,. .. , cI }, servers are of types S = {s1,. .. , sJ }, and there is a bipartite graph G of compatiblities between C, S. The graph has arc (i, j) ∈ G if server type sj has the skill to serve customer type ci. Customers arrive in independent Poisson streams of rates λi, and have absolutely continuous patience distributions Fi. There are nj servers of type sj, and the service times are customer-server-type dependent, the service of a customer of type ci by a server of type sj has a random duration distributed as Gij, with average mij. We use the terminology of queueing theory throughout, but this type of system, with minor modifications, is useful in modeling call centers, manufacturing systems, organ transplants, multimedia servers, and cloud computing [8]. Performance of such systems is highly dependent on the operating policy. We focus here on first come first served (FCFS), where a server is assigned to the longest waiting compatible customer, coupled with assign longest idle server (ALIS), where a customer is assigned to the compatible server that has been idle for the longest time. FCFS-ALIS is widely used, because it is fair to both customers and servers, it is simple to implement, it requires little information about the parameters and the current state of the system, and it is robust under time varying conditions. Our goal here is to develop a structured method to support the design and efficient operation of skill based parallel service systems under FCFS. At this level of generality such systems are highly intractable, no analytic results are expected , and asymptotics, e.g. using many server scaling are called for [12, 10, 7, 13]. We suggest an approximation based on a simplified look at the process — if we discard all arrival *
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MAMA 2013 workshop of ACM Sigmetrics, 2013, Pittsburgh, United States. ACM, ACM SIGMETRICS Performance Evaluation Review, 41 (3), pp.22-24, 2014, 〈10.1145/2567529.2567536〉
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Ivo Adan, Marko Boon, Ana Busic, Jean Mairesse, Gideon Weiss. Queues with Skill Based Parallel Servers and a FCFS Infinite Matching Model. MAMA 2013 workshop of ACM Sigmetrics, 2013, Pittsburgh, United States. ACM, ACM SIGMETRICS Performance Evaluation Review, 41 (3), pp.22-24, 2014, 〈10.1145/2567529.2567536〉. 〈hal-01273894〉

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