System State Distribution of a Finite-Source Retrial Queue with Subscribed Customers

For M/G/1 retrial queues with impatient customers, we review the results, concerning the steady state distribution of the system state, presented in the literature. Since the existing formulas are cumbersome (so their utilization in practice becomes delicate) or the obtaining of these formulas is impossible, we apply the information theoretic techniques for estimating the above mentioned distribution. More concretely, we use the principle of maximum entropy which provides an adequate methodology for computing a unique estimate for an unknown probability distribution based on information expressed in terms of some given mean value constraints.

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NUMBER OF RETRIALS IN A FINITE SOURCE RETRIAL QUEUE WITH UNRELIABLE SERVER

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595914400053 ◽

2014 ◽

Vol 31 (02) ◽

pp. 1440005 ◽

Cited By ~ 13

Author(s):

VELIKA I. DRAGIEVA

Keyword(s):

Steady State ◽

Finite Number ◽

Retrial Queue ◽

Life Time ◽

Retrial Queues ◽

Single Server ◽

System State ◽

Finite Source ◽

Management Optimization ◽

Continue Investigation

The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.

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On the performance of the M1,M2/G1,G2/1 retrial queue with pre-emptive resume policy

Yugoslav journal of operations research ◽

10.2298/yjor130217001b ◽

2015 ◽

Vol 25 (1) ◽

pp. 153-164 ◽

Cited By ~ 4

Author(s):

Leila Boutarfa ◽

Natalia Djellab

Keyword(s):

Manufacturing System ◽

Numerical Study ◽

Retrial Queue ◽

System State ◽

State Distribution ◽

Supplementary Variables ◽

Scheduling Method ◽

To Receive ◽

Service Priority

Priority mechanism is an invaluable scheduling method that allows customers to receive different quality of service. Service priority is clearly today a main feature of the operation of any manufacturing system. We are interested by an M1,M2/G1,G2/1 priority retrial queue with pre-emptive resume policy. For model in question, we discuss the problem of ergodicity and, by using the method of supplementary variables, find the partial generating functions of the steady state system state distribution. Moreover, some pertinent performance measures are obtained and numerical study is also performed.

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