Some Models for Contention Resolution in Cable Networks
NETWORKING '02 Proceedings of the Second International IFIP-TC6 Networking Conference on Networking Technologies, Services, and Protocols; Performance of Computer and Communication Networks; and Mobile and Wireless Communications
Waiting Time Asymptotics in the Single Server Queue with Service in Random Order
Queueing Systems: Theory and Applications
Analysis of the M/G/1 queue with discriminatory random order service policy
Performance Evaluation
Waiting times in queues with relative priorities
Operations Research Letters
Heavy-traffic asymptotics for the single-server queue with random order of service
Operations Research Letters
The equivalence between processor sharing and service in random order
Operations Research Letters
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We study the steady-state queue-length vector in a multiclass single-server queue with relative priorities. Upon service completion, the probability that the next customer to be served is from class k is controlled by class-dependent weights. Once a customer has started service, it is served without interruption until completion. This is a generalization of the random-order-of-service discipline. We investigate the system in a heavy-traffic regime. We first establish a state-space collapse for the scaled queue length vector, that is, the scaled queue length vector is in the limit the product of an exponentially distributed random variable and a deterministic vector. As a direct consequence, we obtain that the scaled number of customers in the system reduces as classes with smaller mean service requirement obtain relatively larger weights. In addition, we present the distribution of the scaled sojourn time of a customer given its class, in heavy traffic.