• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1606-1609
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• 2002

MAC state models appeared with an effort to overcome technical demerits of CDMA in provisioning packet data service. In the scenario of sojourn and transition on MAC states, the design of state sojourn time is a critical issue for an efficient utilization of limited recource; a longer sojourn time leads to more resource being preserved for inactive stations, while more connection components should be recovered with a shorter sojourn time. Thus, the sojourn time at each MAC state must be optimized in consideration of these two conflicting arguments. In this paper, we first present a generic MAC state model. Secondly, based on the generic model, we reveal a relation of inactive period and the delay time of the last packet served in pre- ceding active period and specify a loss function reflect-ing two antinomic features that result from a change of state sojourn time. Using the proposed loss function, we construct a decision problem to find an optima3 rule for state sojourn times. Finally, we present a way of computing Bayes rule by use of the posterior distribution of inactivity duration for given observation on the delay time of last packet. Furthermore, Bayes rules are explicitly expressed for special arrival processes and investigated with respect to traffic load and loss parameters.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1251-1258
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• 2010

For an M/G/1 processor-sharing queue with batch arrivals, Avrachenkov et al. [1] conjectured that the conditional mean sojourn time is concave. However, Kim and Kim [5] showed that this conjecture is not true in general. In this paper, we show that this conjecture is true if the service times have a hyperexponential distribution.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.405-434
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• 1998

We consider an M/M/c queue with two types of custormers, positive customers and negative customers. Positive customers are ordinary ones who upon arrival, join a queue with the intention of getting served and each arrival of negative customer removes a positive customer in the system, if any presents, and then is disappeared immediately. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions of a tagged customer, joinly with the probability that the tagged customer completes his service without being removed are derived under the combinations of various service displines; FCFS, LCFS and PS and removal strategies; RCF, RCH and RCR.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.161-174
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• 2000

The total number of deaths and total sojourn times of African honey bees are studied using semi-markov compartment analysis. This generalizes many existing biological models.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.157-172
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• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.749-757
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• 2012

We consider the M/PH,G/1 queue with two classes of customers in which class-1 customers have deterministic impatience time and have preemptive priority over class-2 customers who are assumed to be infinitely patient. The service times of class-1 and class-2 customers have a phase-type distribution and a general distribution, respectively. We obtain performance measures of class-2 customers such as the queue length distribution, the waiting time distribution and the sojourn time distribution, by analyzing the busy period of class-1 customers. We also compute the moments of the queue length and the waiting and sojourn times.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.547-547
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• 1996

• 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.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.1035-1045
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• 2001

We present two decomposition approximations for the mean sojourn times in open single class queing networks. If there is a single bottleneck station, the approximations are asymptotically exact in both light and heavy traffic. When applied to a Jackson network or an M/G/1 queue, these approximations are exact for all values of the traffic intensity.

• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.511-525
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• 2004

we model communication and computer systems that process interactive and several and several types of background jobs. The scheduling policy in use is to share the processor among all interactive jobs and, at most, one background job of each type at a time according to the process sharing discipline. Background jobs of each type are served on a first-come-first-served basis. Such scheduling policy is called Processor Sharing with Background jobs (PSBJ). In fact, the PSBJ policy is commonly used on many communication and computer systems that allow interactive usage of the systems and process certain jobs in a background mode. In this paper, the stability conditions for the PSBJ policy are given and proved. Since an exact analysis of the policy seems to be very difficult, an approximate analytic model is proposed to obtain the average job sojourn times. The model requires the solution of a set of nonlinear equations, for which an iterative algorithm is given and its convergence is proved. Our results reveal that the model provides excellent estimates of average sojourn times for both interactive and background jobs with a few percent of errors in most of the cases considered.