• Journal of the Korean Statistical Society
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• 제33권2호
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• pp.159-167
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• 2004

We present a simple approach to finding the stationary workload of M/G/1 queues having generalized vacations and exhaustive service discipline. The approach is based on the level crossing technique. According to the approach, all that we need is the workload at the beginning of a busy period. An example system to which we apply the approach is the M/G/1 queue with both multiple vacations and D-policy.

• Journal of applied mathematics & informatics
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• 제6권1호
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• pp.309-320
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• 1999

Models of single-server queues with vacations have been widely used to study the performance of many computer communi-cation and production systems. In this paper we analyze an M/G/1 queue with generalized vacations and exhaustive service. This sys-tem has been shown to possess a stochastic decomposition property. That is the customer waiting time in this system is distributed as the sum of the waiting time in a regular M/G/1 queue with no va-cations and the additional delay due to vacations. Herein a general formula for the additional delay is derived for a wide class of vacation policies. The formula is also extended to cases with multiple types of vacations. Using these new formulas existing results for certain vacation models are easily re-derived and unified.

• 한국경영과학회지
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• 제32권4호
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• pp.89-99
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• 2007

In this paper, an analytic model of a sleep mode operation in the IEEE 802.16e is investigated. A mobile subscriber station(MSS) goes to sleep mode after negotiations with the base station(BS) and wakes up periodically for a short interval to check whether there is downlink traffic to it. If the arrival of traffic is notified, an MSS returns to wake mode. Otherwise, it again enters increased sleep interval which is double as the previous one. In order to consider the situation more practically, we propose the sleep mode starting threshold, during which MSS should await packets before it enters the sleep mode. By modifying the M/G/l with multiple vacations model, energy consumption ratio(ECR) and average packet response time are calculated. Our analytic model provides potential guidance in determining the optimal parameters values such as sleep mode starting threshold, minimal sleep and maximal sleep window.

• 한국경영과학회지
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• 제27권2호
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• pp.51-61
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• 2002

By using the arrival time approach of Chae et at. [6], we derive various performance measures including the queue length distributions (in PGFs) and the waiting time distributions (in LST and PGF) for both M$^{x}$ /G/1 and Geo$^{x}$ /G/1 queueing systems, both under the assumption that the server, when it becomes idle, takes multiple vacations up to a random maximum number. This is an extension of both Choudhury[7] and Zhang and Tian [11]. A few mistakes in Zhang and Tian are corrected and meaningful interpretations are supplemented.

• Journal of the Korean Statistical Society
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• 제36권2호
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• pp.285-297
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• 2007

We consider the $P_{\lambda}^M-service$ policy for an M/G/1 queueing system in which the workload is monitored randomly at discrete points in time. If the level of the workload exceeds a threshold ${\lambda}$ when it is monitored, then the service rate is increased from 1 to M instantaneously and is kept as M until the workload reaches zero. By using level-crossing arguments, we obtain explicit expressions for the stationary distribution of the workload in the system.

• 한국경영과학회지
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• 제27권2호
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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.

• Management Science and Financial Engineering
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• 제12권2호
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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.

• Journal of applied mathematics & informatics
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• 제6권3호
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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 applied mathematics & informatics
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• 제5권1호
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• pp.1-12
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• 1998

We consider G/M/1 queues with multiple vacation disci-pline where at the end of every busy period the server stays idle in the system for a period of time called changeover time and then follows a vacation if there is no arrival during the changeover time. The vaca-tion time has a hyperexponential distribution. By using the methods of the shift operator and supplementary variable we explicitly obtain the queue length probabilities at arrival time points and arbitrary time points simultaneously.

• 대한산업공학회지
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• 제33권4호
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• pp.419-423
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• 2007

In this paper, we consider the M/G/1 queueing system with randomized control of T-policy. Whenever the busy period ends, the server is turned off and takes multiple vacations whose interval is fixed time T with probability p or stays on and waits for arriving customers with probability 1-p. We introduce the cost function and determine the optimal combination of (p, T) to minimize the average cost per unit time.