• Title, Summary, Keyword: vacation queue

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A Batch Arrival Queue with Bernoulli Vacation Schedule under Multiple Vacation Policy

  • Choudhury Gautam;Madan Kailash C.
    • Management Science and Financial Engineering
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    • v.12 no.2
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    • pp.1-18
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    • 2006
  • We consider an $M^x/G/1$ queueing system with Bernoulli vacation schedule under multiple vacation policy. where after each vacation completion or service completion the server takes sequence of vacations until a batch of new customer arrive. This generalizes both $M^x/G/1$ queueing system with multiple vacation as well as M/G/1 Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further attempts have been made to unify the results of related batch arrival vacation models.

A Batch Arrival Queue with a Random Setup Time Under Bernoulli Vacation Schedule

  • Choudhury, Gautam;Tadj, Lotfi;Paul, Maduchanda
    • Management Science and Financial Engineering
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    • v.15 no.2
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    • pp.1-21
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    • 2009
  • We consider an $M^x/G/1$ queueing system with a random setup time under Bernoulli vacation schedule, where the service of the first unit at the completion of each busy period or a vacation period is preceded by a random setup time, on completion of which service starts. However, after each service completion, the server may take a vacation with probability p or remain in the system to provide next service, if any, with probability (1-p). This generalizes both the $M^x/G/1$ queueing system with a random setup time as well as the Bernoulli vacation model. We carryout an extensive analysis for the queue size distributions at various epochs. Further, attempts have been made to unify the results of related batch arrival vacation models.

Analysis of the M/G/1 Priority Queue with vacation period depending on the Customer's arrival (휴가기간이 고객의 도착에 영향을 받는 휴가형 우선순위 M/G/1 대기행렬 분석)

  • Jeong, Bo-Young;Park, Jong-Hun;Baek, Jang-Hyun;Lie, Chang-Hoon
    • IE interfaces
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    • v.25 no.3
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    • pp.283-289
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    • 2012
  • M/G/1 queue with server vacations period depending on the previous vacation and customer's arrival is considered. Most existing studies on M/G/1 queue with server vacations assume that server vacations are independent of customers' arrival. However, some vacations are terminated by some class of customers' arrival in certain queueing systems. In this paper, therefore, we investigate M/G/1 queue with server vacations where each vacation period has different distribution and vacation length is influenced by customers' arrival. Laplace-Stieltjes transform of the waiting time distribution and the distribution of number of customers waiting for each class of customers are respectively derived. As performance measures, mean waiting time and average number of customers waiting for each class of customers are also derived.

Steady State Probabilities for the Server Vacation Model with Group Arrivals and under Control operating Policy (제어운영 정책하에 있는 집단으로 도착하는 서어버 휴가 모형의 안정상태 확률)

  • 이효성
    • Journal of the Korean Operations Research and Management Science Society
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    • v.16 no.2
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    • pp.36-48
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    • 1991
  • In this study, an efficient algorithm is developed to compute steady state probabilities for the following M$_{x}$G/1 server vacation system under control-operating poligy: At the end of a busy period, the server takes a sequence of vacations, each for a random amount of time. At the end of each vacation, he inspects the length of the queue. If the queue length at this time is equal to or greater than a prespecified threshold value r, he begins to serve the queue until it is empty.y.

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APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS

  • SHIN, YANG WOO;MOON, DUG HEE
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.19 no.4
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    • pp.443-457
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    • 2015
  • We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.

STABILITY OF MAP/PH/c/K QUEUE WITH CUSTOMER RETRIALS AND SERVER VACATIONS

  • Shin, Yang Woo
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.4
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    • pp.985-1004
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    • 2016
  • We consider the MAP/PH/c/K queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.

A SINGLE SERVER RETRIAL QUEUE WITH VACATION

  • Kalyanaraman, R.;Murugan, S. Pazhani Bala
    • Journal of applied mathematics & informatics
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    • v.26 no.3_4
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    • pp.721-732
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    • 2008
  • A single server infinite capacity queueing system with Poisson arrival and a general service time distribution along with repeated attempt and server vacation is considered. We made a comprehensive analysis of the system including ergodicity and limiting behaviour. Some operating characteristics are derived and numerical results are presented to test the feasibility of the queueing model.

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GENERAL FORMULAS OF SOME VACATION MODELS

  • Lim, Jong-Seul
    • Journal of applied mathematics & informatics
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    • v.26 no.1_2
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    • pp.389-393
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    • 2008
  • This paper describes a single-server queue where the server is unavailable during some intervals of time, which is referred to as vacations. The major contribution of this work is to derive general formulas for the additional delay in the vacation models of the single vacations, head of line priority queues with non-preemptive service, and multiple vacations and idle time.

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Heuristic Approach to the Mean Waiting Time of $Geo^x/G/1$ Vacation Queues with N-policy and Setup Time (휴리스틱 방법을 이용한 N정책과 준비기간을 갖는 휴가형 $Geo^x/G/1$ 모형의 평균대기시간 분석)

  • Lee, Sung-Hee;Kim, Sung-Jin;Chae, Kyung-Chul
    • Journal of the Korean Operations Research and Management Science Society
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    • v.32 no.1
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    • pp.53-60
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    • 2007
  • We consider the discrete-time $Geo^x/G/1$ queues under N-policy with multiple vacations (a single vacation) and setup time. In this queueing system, the server takes multiple vacations (a single vacation) whenever the system becomes empty, and he begins to serve the customers after setup time only if the queue length is at least a predetermined threshold value N. Using the heuristic approach, we derive the mean waiting time for both vacation models. We demonstrate that the heuristic approach is also useful for the discrete-time queues.

Mean Waiting Time Analysis of Cyclic Server System under N-Policy (N-정책하의 순환 서비스시스템의 평균대기시간 분석)

  • 홍정완;이창훈
    • Journal of the Korean Operations Research and Management Science Society
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    • v.18 no.3
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    • pp.51-63
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    • 1993
  • We consider a cyclid server system under N-policy. This system consists of multiple queues served in a cyclic order by a single server. In this paper, we consider the following control policy. Every time server polls one queue, the server inspects the state of the queue. If the total number of units is found to have reached or exceeded a pre-specified value, the server begins to serve the queue until it is empty. As soon as the queue becomes empty, the server polls next queue. An approximate analysis of this system is presented. Sever vacation model is used as an analytical tool. However, server vacation periods are considered to be dependent on the service times of respective queues. The results obtained from the approximate analysis are ompared with simulation results.

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