Continuity of Large Closed Queueing Networks with Bottlenecks
نویسنده
چکیده
This paper studies a closed queueing network containing a hub (a state dependent queueing system with service depending on the number of units residing here) and k satellite stations, which are GI/M/1 queueing systems. The number of units in the system, N , is assumed to be large. After service completion in the hub, a unit visits a satellite station j, 1 ≤ j ≤ k, with probability pj , and, after the service completion there, returns to the hub. The parameters of service times in the satellite stations and in the hub are proportional to 1 N . One of the satellite stations is assumed to be a bottleneck station, while others are non-bottleneck. The paper establishes the continuity of the queue-length processes in non-bottleneck satellite stations of the network when the service times in the hub are close in certain sense (exactly defined in the paper) to the exponential distribution. 1991 Mathematics Subject Classification. 60K25, 90B18, 60E15.
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