• Journal of the Korea Society for Simulation
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• v.16 no.2
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• pp.75-81
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• 2007

Previous queue inference has been studied with some limits. Larson's inference engine, which is the basis for this paper, also processed with basic assumption that arrival process is poisson process. Our inference method, which relaxes the poisson process assumption, must be a useful tool for looking into unobservable inside of queueing systems, as well as calculating accurate system performance. This paper employs these inference methods and proves the validity. Then we apply this method to system analysis for more complicated models. At first, we suggest methods to system with known number of servers, then expand to unknown number of servers. For validating our inference approach, we run some simulation models and compare true values with our results.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.523-533
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• 2006

We analyze two finite buffers queueing system with priority scheduling dependent upon queue length. Customers are classified into two types ( type-l and type-2 ) according to their characteristics. Here, the customers can be considered as traffics such as voice and data in telecommunication networks. In order to support customers with characteristics of burstiness and time-correlation between interarrival, the arrival of the type-2 customer is assumed to be an Markov- modulated Poisson process(MMPP). The service order of customers in each buffer is determined by the queue length of two buffers. Methods of embedded Markov chain and supplementary variable give us information for queue length of two buffers. Finally, performance measures such as loss and mean delay are derived.

• 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.

• 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.39 no.5_6
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• pp.601-616
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• 2021

Retrial queueing models have been studied extensively in the literature. These have many practical applications, especially in service sectors. However, retrial queueing models have their own limitations. Typically, analyzing such models involve level-dependent quasi-birth-and-death processes, and hence some form of a truncation or an approximate method or simulation approach is needed to study in steady-state. Secondly, in general, the customers are not served on a first-come-first-served basis. The latter is the case when a new arrival may find a free server while prior arrivals are waiting in the retrial orbit due to the servers being busy during their arrivals. In this paper, we take a different approach to the study of multi-server retrial queues in which the signals are generated in such a way to provide a reasonably fair treatment to all the customers seeking service. Further, this approach makes the study to be level-independent quasi-birth-and-death process. This approach is different from any considered in the literature. Using matrix-analytic methods we analyze MAP/M/c-type retrial queueing models along with Poisson signals in steady-state. Illustrative numerical examples including a comparison with previously published retrial queues are presented and they show marked improvements in providing a quality of service to the customers.

• Journal of Korea Society of Industrial Information Systems
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• v.12 no.4
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• pp.107-118
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• 2007

A single-server queueing model with infinite buffer and batch arrival of customers is considered. In contrast to the standard batch arrival when a whole batch arrives into the system at one epoch, we assume that the customers of an accepted batch arrive one-by one in exponentially distributed times. Service time is exponentially distributed. Flow of batches is the stationary Poisson arrival process. Batch size distribution is geometric. The number of batches, which can be admitted into the system simultaneously, is subject of control. Analysis of the joint distribution of the number batches and customers in the system and sojourn time distribution is implemented by means of the matrix technique and method of catastrophes. Effect of control on the main performance measures of the system is demonstrated numerically.

• Journal of Information Processing Systems
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• v.7 no.4
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• pp.653-678
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• 2011

WiMAX is intended for fourth generation wireless mobile communications where a group of users are provided with a connection and a fixed length queue. In present literature traffic of such network is analyzed based on the generator matrix of the Markov Arrival Process (MAP). In this paper a simple analytical technique of the two dimensional Markov chain is used to obtain the trajectory of the congestion of the network as a function of a traffic parameter. Finally, a two state phase dependent arrival process is considered to evaluate probability states. The entire analysis is kept independent of modulation and coding schemes.

• Management Science and Financial Engineering
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• v.2 no.1
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• pp.123-145
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• 1996

We consider a priority-based multiclass queue with probabilistic feed-back. There are J service stations. Each customer belongs to one of the several priority classes, and the customers of each class arrive at each station in a Poisson process. A single server serves queued customers on a priority basis with a nonpreemptive scheduling discipline. The customers who complete their services feed back to the system instantaneously and join one of the queues of the stations or depart from the system according to a given probability. In this paper, we propose a new method to simplify the analysis of these queueing systems. By the analysis of busy periods and regenerative processes, we clarify the underlying system structure, and systematically obtain the mean for the sojourn time, i.e., the time from the arrival to the departure from the system, of a customer at every station. The mean for the number of customers queued in each station at an arbitrary time is also obtained simultaneously.

• ETRI Journal
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• v.31 no.1
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• pp.86-88
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• 2009

In this letter, we consider an m-node tandem queue (queues in series) with a Poisson arrival process and either deterministic or non-overlapping service times. With the assumption that each node has a finite buffer except for the first node, we show the non-increasing convex property of stationary waiting time with respect to the finite buffer capacities. We apply it to an optimization problem which determines the smallest buffer capacities subject to probabilistic constraints on stationary waiting times.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.28 no.4
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• pp.134-141
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• 2005

Due to the complexity and stochastic nature of automated warehousing system, items are usually queued up at I/O point. We introduce a storage/retrieval policy : dual-command. We present quick approximations to queueing phenomena under these policies. It is assumed that the storage and retrieval arrival pattern follow the same poisson process. We also assumed that storage queue and retrieval queue being operated separately. The approximation attempts are performed under the proposed storage/retrieval policies after we derive S/R machine travel time distributions.