NDLI: A repairable Geo X /G/1 retrial queue with Bernoulli feedback and impatient customers

Content Provider	Springer Nature Link
Author	Liu, Zai ming Gao, Shan
Copyright Year	2014
Abstract	This paper deals with a discrete-time batch arrival retrial queue with the server subject to starting failures. Different from standard batch arrival retrial queues with starting failures, we assume that each customer after service either immediately returns to the orbit for another service with probability θ or leaves the system forever with probability 1 − θ (0 ≤ θ < 1). On the other hand, if the server is started unsuccessfully by a customer (external or repeated), the server is sent to repair immediately and the customer either joins the orbit with probability q or leaves the system forever with probability 1 − q (0 ≤ q < 1). Firstly, we introduce an embedded Markov chain and obtain the necessary and sufficient condition for ergodicity of this embedded Markov chain. Secondly, we derive the steady-state joint distribution of the server state and the number of customers in the system/orbit at arbitrary time. We also derive a stochastic decomposition law. In the special case of individual arrivals, we develop recursive formulae for calculating the steady-state distribution of the orbit size. Besides, we investigate the relation between our discrete-time system and its continuous counterpart. Finally, some numerical examples show the influence of the parameters on the mean orbit size.
Ending Page	222
Page Count	18
Starting Page	205
File Format	PDF
ISSN	01689673
e-ISSN	16183932
Journal	Acta Mathematicae Applicatae Sinica
Issue Number	1
Volume Number	30
Language	English
Publisher	Springer Berlin Heidelberg
Publisher Date	2014-04-26
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	discrete-time queue starting failure steady state Queues and service Theoretical, Mathematical and Computational Physics retrial queue Bernoulli feedback Applications of Mathematics Math Applications in Computer Science Queueing theory
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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