• 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.

• 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.

• Journal of Korean Institute of Industrial Engineers
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• v.22 no.1
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• pp.95-104
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• 1996

We consider a two-phase queueing system with generalized vacation. Poisson arrivals receive a batch type service in the first phase and individual services in the second phase. The server takes generalized vacation when the system becomes empty. Generalized vacation includes single vacation, multiple vacation, and other types. We consider both gated batch service and exhaustive batch service. This is an extension of the model presented by Selvam and Sivasankaran [6].

• 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.

• Journal of Korea Society of Industrial Information Systems
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• v.25 no.1
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• pp.89-99
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• 2020

In this paper, we consider a dyadic server control policy that combines workload control and single vacation. Customer arrives at the system with Bernoulli process, waits until his or her turn, and then receives service on FCFS(First come first served) discipline. If there is no customer to serve in the system, the idle single server spends a vacation of discrete random variable V. If the total service times of the waiting customers at the end of vacation exceeds predetermined workload threshold D, the server starts service immediately, and if the total workload of the system at the end of the vacation is less than or equal to D, the server stands by until the workload exceeds threshold and becomes busy. For the discrete-time Geo/G/1 queueing system operated under this dyadic server control policy, an idle period is analyzed and the steady-state queue length distribution is derived in a form of generating function.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.42 no.4
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• pp.91-105
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• 2019

Discrete-time Queueing models are frequently utilized to analyze the performance of computing and communication systems. The length of busy period is one of important performance measures for such systems. In this paper, we consider the busy period of the Geo/Geo/1/K queue with a single vacation. We derive the moments of the length of the busy (idle) period, the number of customers who arrive and enter the system during the busy (idle) period and the number of customers who arrive but are lost due to no vacancies in the system for both early arrival system (EAS) and late arrival system (LAS). In order to do this, recursive equations for the joint probability generating function of the busy period of the Geo/Geo/1/K queue starting with n, 1 ≤ n ≤ K, customers, the number of customers who arrive and enter the system, and arrive but are lost during that busy period are constructed. Using the result of the busy period analysis, we also numerically study differences of various performance measures between EAS and LAS. This numerical study shows that the performance gap between EAS and LAS increases as the system capacity K decrease, and the arrival rate (probability) approaches the service rate (probability). This performance gap also decreases as the vacation rate (probability) decrease, but it does not shrink to zero.

• 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.

• 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.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.2
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• pp.111-121
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• 2002

In this paper, we analyze an M$^{x}$ /G/1 with three types of vacation periods including setup time. Three types of vacations are : N-policy, single vacation, and multiple vacation. We consider compound poisson arrival process and general service time, where the server starts his service when a setup is completed. We find the PGF of the number of customers in system and LST of waiting time, with welch we obtain their means. A decomposition property for the system sloe and waiting time is described also.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1993.04a
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• pp.229-229
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• 1993