Jongho Bae

The Virtual Waiting Time of the M / G / 1 Queue with Impatient Customers

The M/G/1 queue with impatient customers is studied. The complete formula of the limiting distribution of the virtual waiting time is derived explicitly. The expected busy period of the queue is also obtained by using a martingale argument.

A PλM-policy for an M/G/1 queueing system☆

Abstract We introduce P λ M -service policy for an M / G /1 queueing system. The stationary distribution of the workload under this policy is explicitly obtained through a decomposition technique, renewal reward theorem, and level crossing argument.

Busy Periods of Poisson Arrival Queues with Loss

We consider two queues with loss, one is the finite dam with Poisson arrivals and the other is the M/G/1 queue with impatient customers. We use the method of Kolmogorovs backward differential equation and construct a type of renewal equation to obtain the Laplace transform of busy(or wet) period in both queues. As a consequence, we provide the explicit forms of expected busy periods.

The Approximation for the Auxiliary Renewal Function

The auxiliary renewal function has an important role in analyzng queues in which the either of the inter-arrival time and the service time of customers is not exponential. As like the renewal function, the auxiliary renewal function is hard to compute although it can be defined theoretically. In this paper, we suggest two approximations for auxiliary renewal function and compare the two with the true value of auxiliary renewal function which can be computed in some special cases.

An optimal service rate in a Poisson arrival queue with two-stage service policy*

Abstract.We consider a two-stage service policy for a Poisson arrival queueing system. The idle server starts to work with ordinary service rate when a customer arrives. If the number of customers in the system reaches N, the service rate gets faster and continues until the system becomes empty. Otherwise, the server finishes the busy period with ordinary service rate. After assigning various operating costs to the system, we show that there exists a unique fast service rate minimizing the long-run average cost per unit time.

A repair policy with limited number of minimal repairs

The imperfect repair model of Brown and Proschan [2] is modified by restricting the number of consecutive al repairs by n(n=0,1,2,...). We extend the earlier analysis by studying the preservation of ageing properties of the modified model and by obtaining several interesting monotonicities of long-run average time between succes-sive failures.

An Approximation to the Overshoot in M/E n /1 Queues

In this paper, we propose an approximation to the overshoot in M//1 queues. Overshoot means the size of excess over the threshold when the workload process of an M//1 queue exceeds a prespecified threshold. The distribution, and moments of overshoot have an important role in solving some kind of optimization problems. For the approximation to the overshoot, we propose a formula that is a convex sum of the service time distribution and an exponential distribution. We also do a numerical study to check how exactly the proposed formula approximates the overshoot.

A queueing system with -service policy

We consider a G/M/1G/M/1 queue with PλM-service policy, which is a two-stage service policy. The stationary distribution of the workload under the policy is obtained through a decomposition technique and the analogy of level-crossings of the corresponding M/G/1M/G/1 queueing system.