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

• 제어로봇시스템학회:학술대회논문집
• /
• 1989.10a
• /
• pp.524-529
• /
• 1989

In this paper, an approximate sojourn time distribution is obtained for cyclic service systems. We consider symmetric and limited service systems in which each queue has an infinite capacity. The combined service time is defined which consists of the frame service time and server waiting time that is approximated by two cases of the uniform and exponential distributions. The approximate sojourn time distribution is obtained from the Pollaczek-Khinchine formula where the combined service time is used for the service time in the M/G/I model. And some numerical examples are given to validate the suggested approximate analysis.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.19 no.3
• /
• pp.93-109
• /
• 1994

Even though sojourn time distributions are essential information in analyzing queueing networks, there are few methods to compute them accurately in non-product form queueing networks. In this study, we model the location process of a typical customer as a GMPH semi-Markov chain and develop computationally useful formula for the transition function and the first-passage time distribution in the GMPH semi-Markov chain. We use the formula to develop an effcient method for approximating sojourn time distributions in the non-product form queueing networks under quite general situation. We demonstrate its validity through numerical examples.

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

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

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.277-292
• /
• 2006

We consider a single-server queue with service time distribution of phase type where positive customers, negative customers and disasters arrive according to a Markovian arrival process with marked transitions (MMAP). We derive simple formulae for the stationary queue length distributions. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions under the combinations of removal policies and service disciplines are also obtained by using the absorption time distribution of a Markov chain.

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

• Communications for Statistical Applications and Methods
• /
• v.25 no.4
• /
• pp.443-451
• /
• 2018

$P^M_{\lambda}$-service policy is a workload dependent hysteretic policy. The policy has two service states comprised of the ordinary stage and the fast stage. An ordinary service stage is initiated by the arrival of a customer in an idle state. When the workload of the server surpasses threshold ${\lambda}$, the ordinary service stage changes to the fast service state, and it continues until the system is empty. These service stages alternate in this manner. When the cost of changing service stages is high, the hysteretic policy is more efficient than the threshold policy, where a service stage changes immediately into the other service stage at either case of the workload's surpassing or crossing down a threshold. $P^M_{\lambda}$-service policy is a modification of $P^M_{\lambda}$-policy proposed to control finite dams, and also an extension of the well-known D-policy. The distributions of the stationary workload of $P^M_{\lambda}$-service policy and its variants are studied well. However, there is no known result on the sojourn time distribution. We prove that there is a relation between the sojourn time of a customer and the first up-crossing time of the workload process over the threshold ${\lambda}$ after the arrival of the customer. Using the relation and the duality of M/G/1 and G/M/1 queues, we obtain conditional sojourn time distributions in M/G/1 and G/M/1 queues under the policy.

• Industrial Engineering and Management Systems
• /
• v.12 no.3
• /
• pp.281-287
• /
• 2013

In this paper, we introduce a roots method that uses the roots inside the unit circle of the associated characteristics equation to evaluate the steady-state system-length distribution at three epochs (pre-arrival, arbitrary, and post-departure) and sojourn-time distribution in GI/PH/1 queueing model. It is very important for an air base to inspect airplane oil because low-quality oil leads to drop or breakdown of an airplane. Since airplane oil inspection is composed of several inspection steps, it sometimes causes train congestion and delay of inventory replenishments. We analyzed interarrival time and inspection (service) time of oil supply from the actual data which is given from one of the ROKAF's (Republic of Korea Air Force) bases. We found that interarrival time of oil follows a normal distribution with a small deviation, and the service time follows phase-type distribution, which was first introduced by Neuts to deal with the shortfalls of exponential distributions. Finally, we applied the GI/PH/1 queueing model to the oil train congestion problem and analyzed the distributions of the number of customers (oil trains) in the queue and their mean sojourn-time using the roots method suggested by Chaudhry for the model GI/C-MSP/1.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1998.10a
• /
• pp.186-189
• /
• 1998

In this paper, we provide a mathematical formulation to describe the random mobility of users in cellular radio systems. With this, we can also study tile cell sojourn time (CST) distribution as well as the channel holding time (CHT) distribution. The study on user mobility enables to improve the resource management in cellular radio systems. We provide a versatile analysis tool that improves the limit of simplified analyses.