Analysis of polling systems
Boundary value problems in queueing theory
Queueing Systems: Theory and Applications
Queuing analysis of polling models
ACM Computing Surveys (CSUR)
Exact results for the cyclic-service queue with a Bernoulli schedule
Performance Evaluation
Two Symmmetric Queues with Alternating Service and Switching Times
Performance '84 Proceedings of the Tenth International Symposium on Computer Performance Modelling, Measurement and Evaluation
Two Queues with Alternating Service Periods
Performance '87 Proceedings of the 12th IFIP WG 7.3 International Symposium on Computer Performance Modelling, Measurement and Evaluation
Queueing Systems: Theory and Applications
A Tandem Queue with Coupled Processors: Computational Issues
Queueing Systems: Theory and Applications
Approximation of discrete-time polling systems via structured Markov chains
Proceedings of the Fourth International ICST Conference on Performance Evaluation Methodologies and Tools
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In this paper, we present a detailed analysis of a cyclic-service queueing system consisting of two parallel queues, and a single server. The server serves the two queues with a Bernoulli service schedule described as follows. At the beginning of each visit to a queue, the server always serves a customer. At each epoch of service completion in the ith queue at which the queue is not empty, the server makes a random decision: with probability p_{i}, it serves the next customer; with probability 1-p_{i}, it switches to the other queue. The server takes switching times in its transition from one queue to the other. We derive the generating functions of the joint stationary queue-length distribution at service completion instants, by using the approach of the boundary value problem for complex variables. We also determine the Laplace–Stieltjes transforms of waiting time distributions for both queues, and obtain their mean waiting times.