• 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.

M/G/1 Queueing System wish Vacation and Limited-1 Service Policy

  • Lee, B-L.;W. Ryu;Kim, D-U.;Park, B.U.;J-W. Chung
    • Journal of the Korean Statistical Society
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    • v.30 no.4
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    • pp.661-666
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    • 2001
  • In this paper we consider an M/G/1 queue where the server of the system has a vacation time and the service policy is limited-1. In this system, upon termination of a vacation the server returns to the queue and serves at most one message in the queue before taking another vacation. We consider two models. In the first, if the sever finds the queue empty at the end of a cacation, then the sever immediately takes another vacation. In the second model, if no message have arrived during a vacation, the sever waits for the first arrival to serve. The analysis of this system is particularly useful for a priority class polling system. We derive Laplace-Stieltjes transforms of the waiting time for both models, and compare their mean waiting times.

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Balking Phenomenon in the $M^{[x]}/G/1$ Vacation Queue

  • Madan, Kailash C.
    • Journal of the Korean Statistical Society
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    • v.31 no.4
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    • pp.491-507
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    • 2002
  • We analyze a single server bulk input queue with optional server vacations under a single vacation policy and balking phenomenon. The service times of the customers as well as the vacation times of the server have been assumed to be arbitrary (general). We further assume that not all arriving batches join the system during server's vacation periods. The supplementary variable technique is employed to obtain time-dependent probability generating functions of the queue size as well as the system size in terms of their Laplace transforms. For the steady state, we obtain probability generating functions of the queue size as well as the system size, the expected number of customers and the expected waiting time of the customers in the queue as well as the system, all in explicit and closed forms. Some special cases are discussed and some known results have been derived.

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.

M/G/1 QUEUE WITH COMPLEX VACATION POLICIES

  • Lim, Jong-Seul;Oh, Choon-Suk
    • Journal of applied mathematics & informatics
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    • v.6 no.3
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    • pp.943-952
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    • 1999
  • Models of single-server queues with vacation have been widely used to study the performance of many computer communica-tion and production system. In this paper we use the formula for a wide class of vacation policies and multiple types of vacations based on the M/G/1 queue with generalized vacations and exhaustive service. furthermore we derive the waiting times for many complex vacation policies which would otherwise be to analyze. These new results are also applicable to other related queueing models. if they conform with the basic model considered in this paper.

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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