An M^[X]/G(a,b)/1 queueing system with unreliable server, stand-by server, restricted arrivals, variant threshold policy for vacations

This work considers a queueing system with N-policy and unreliable server, where potential customers arrive at the system according to Poisson process. If there is no customer waiting in the system, instead of shutting down, the server turns into dormant state and does not afford service until the number of customers is accumulated to a certain threshold. And in the working state, the server is apt to breakdown and affords service again only after it is repaired. According to whether the server state is observable or not, the numerical optimal arrival rates are computed to maximize the social welfare and throughput of the system. The results illustrate their tendency in two cases so that the manager has a strong ability to decide which is more crucial in making management decision.

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Queueing system with an absolutely unreliable server and a variable stream of customers

Cybernetics and Systems Analysis ◽

10.1007/bf02366929 ◽

1995 ◽

Vol 31 (2) ◽

pp. 285-292

Author(s):

V. Yu. Kotlyar

Keyword(s):

Queueing System ◽

Unreliable Server

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Some characterizations of the exponential and geometric distributions arising in a queueing system with an unreliable server

Journal of Applied Probability ◽

10.2307/3214529 ◽

1993 ◽

Vol 30 (4) ◽

pp. 985-990 ◽

Cited By ~ 2

Author(s):

Wen-Jang Huang ◽

Jyh-Ming Shoung

Keyword(s):

Queueing System ◽

Unreliable Server

In this article, we generalize results by Dimitrov and Khalil (1990), Khalil et al. (1991), and van Harn and Steutel (1991) and obtain some characterizations of the exponential and geometric laws.

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Characterizations of the Exponential Distribution via the Blocking Time in a Queueing System with an Unreliable Server

Journal of Applied Probability ◽

10.1239/jap/1032192567 ◽

1998 ◽

Vol 35 (1) ◽

pp. 236-239 ◽

Cited By ~ 1

Author(s):

Jian-Lun Xu

Keyword(s):

Exponential Distribution ◽

Service Time ◽

Coefficient Of Variation ◽

Queueing System ◽

Random Variables ◽

Unreliable Server ◽

Failure Times ◽

Server Failure

The characterization of the exponential distribution via the coefficient of the variation of the blocking time in a queueing system with an unreliable server, as given by Lin (1993), is improved by substantially weakening the conditions. Based on the coefficient of variation of certain random variables, including the blocking time, the normal service time and the minimum of the normal service and the server failure times, two new characterizations of the exponential distribution are obtained.

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Confidence Intervals for Performance Measures of M/M/1 Queue with Constant Retrial Policy

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595915500463 ◽

2015 ◽

Vol 32 (06) ◽

pp. 1550046

Author(s):

Dmitry Efrosinin ◽

Anastasia Winkler ◽

Pinzger Martin

Keyword(s):

Performance Measures ◽

Queueing System ◽

Retrial Queue ◽

Threshold Level ◽

Stationary Regime ◽

Parametric Estimation ◽

Threshold Policy ◽

System Parameters ◽

Number Of Customers ◽

The Given

We consider the problem of estimation and confidence interval construction of a Markovian controllable queueing system with unreliable server and constant retrial policy. For the fully observable system the standard parametric estimation technique is used. The arrived customer finding a free server either gets service immediately or joins a retrial queue. The customer at the head of the retrial queue is allowed to retry for service. When the server is busy, it is subject to breakdowns. In a failed state the server can be repaired with respect to the threshold policy: the repair starts when the number of customers in the system reaches a fixed threshold level. To obtain the estimates for the system parameters, performance measures and optimal threshold level we analyze the system in a stationary regime. The performance measures including average cost function for the given cost structure are presented in a closed matrix form.

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