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Author

Liyuan Zhang

Bio: Liyuan Zhang is an academic researcher. The author has contributed to research in topics: M/G/1 queue. The author has an hindex of 1, co-authored 1 publications receiving 16 citations.
Topics: M/G/1 queue

Papers
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Journal ArticleDOI
TL;DR: This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs, and applies the embedded Markov chain to obtain the necessary andcient condition for the stability of the system.
Abstract: This paper considers an M/G/1 retrial G-queue with general retrial times, in which the server is subject to working breakdowns and repairs. If the system is not empty during a normal service period, the arrival of a negative customer can cause the server breakdown, and the failed server still works at a lower service rate rather than stopping the service completely. Applying the embedded Markov chain, we obtain the necessary and sufficient condition for the stability of the system. Using the supplementary variable method, we deal with the generating functions of the number of customers in the orbit. Various system performance measures are also developed. Finally, some numerical examples and a cost optimization analysis are presented.

20 citations


Cited by
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Journal ArticleDOI
TL;DR: An overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique and factors causing service interruption such as unreliable server and server vacation are presented.
Abstract: In most of the queueing models, service is considered to be complete without any interruption. But in reality, queueing systems are subject to interruptions due to failure of server or any other cause. In the present article, we present an overview and literature survey on the performance modeling and analysis of single server, general service queueing system with service interruption using supplementary variable technique. The factors causing service interruption such as unreliable server and server vacation are elaborated. The brief of supplementary variable technique to establish the queue size distribution is explained for single server non-Markovian queueing models by incorporating the features of service interruption. The basic concepts and review of literature on the queues with server breakdown and/or vacationing server are described. The research works done during last 10 years (2010–2019) on queues with service interruption involving many other key concepts namely Bernoulli vacation, multiple vacation, bulk arrival, discouragement, etc. and queueing scenarios of service interruption are reported. Some specific applications are also highlighted.

16 citations

Journal ArticleDOI
TL;DR: This paper applies the generating function method to derive the joint distribution of the server state and the orbit length in the steady state, and obtains some performance measures.
Abstract: The present paper deals with the performance evaluation of an M/M/1 retrial queue with collisions, transmission errors and unreliable server. To the best of our knowledge, there are no works that h...

8 citations

Journal ArticleDOI
TL;DR: This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2) using the matrix geometric method to compute the stationary distribution of system size and presents numerical results showing the effects of various parameters on the approximate optimal service rates.
Abstract: This paper presents a steady-state analysis of an M/M/2 queue with heterogeneous servers (Server 1 and Server 2). Server 1 is reliable and may leave for a vacation when the system becomes empty. Se...

6 citations

Journal ArticleDOI
TL;DR: In this paper , the performance analysis of a non-Markovian machining system comprised of operating and standby machines together and functioning under N-policy for vacation is presented, where the repairman's vacation policy to return to the repair job as soon as the workload reaches a pre-defined threshold.

3 citations