Genji Yamazaki

Hybrid evolutionary method for capacitated location-allocation problem

Abstract Location-allocation model is widely applied for facility location design in practice. In this paper, we discuss an extension of location-allocation model which has capacity constraints and propose a hybrid evolutionary method to solve it which absorbs ideas from both genetic algorithms (GAs) and evolutionary strategy (ES) as well as combined with efficient traditional optimization techniques. It is shown that the proposed method is effective in finding global or near global solutions by numerical simulations.

Characterization of optimal order of servers in a tandem queue with blocking

Consider a tandem queueing system with m stages with no intermediate storage space between stages j and j + 1, j=1,...,m -1. There is an unlimited supply of customers in front of the first stage and the output buffer storage for stage m has an unlimited capacity. For this system we consider the problem of allocating m servers, one to each of these m stages such that the customer departure process from the system is stochastically maximized. In this regard we have shown that if the service times of the servers are comparable in the reversed hazard rate (or the usual stochastic) ordering then there exists an optimal allocation where the server allocated to the first stage has a larger mean service time than that assigned to the second stage. These results complement the recent results of Huang and Weiss (1990) and Yamazaki, Sakasegawa and Shanthikumar (1989).

Moments in infinite channel queues

We consider a new approach to the problem of evaluating the moments of the steady-state number of customers in system B for an infinite channel queue having general input. Our new approach uses the rate conservation law. As a consequence, we show that for a variety of G/GI/∞ queues, Var (B) < ∞ as long as service times have finite first moment. In addition, we give some ordering relations for the variance of B when comparing two alternative systems with convex ordered inter-arrival time distributions.

The equality of the workload and total attained waiting time in average

It has recently been shown that, for the FCFS G/G/I queue, the workload and attained waiting time of a customer in service have the same stationary distribution. We show that, for a general queueing system setting, the workload and total attained waiting time of customers in service are identical in average but the equality of the distributions is not true in general except for the FCFS GiG/I queue. QUEUE; SAMPLE AVERAGE

Invariance relations in single server queues with LCFS service discipline

This paper is concerned with single server queues having LCFS service discipline. We give a condition to hold an invariance relation between time and customer average queue length distributions in the queues. The relation is a generalization of that in an ordinary GI/M/1 queue. We compare the queue length distributions for different single server queues with finite waiting space under the same arrival process and service requirement distribution of customer and derive invariance relations among them.

Decomposability in queues with background states

A symmetric queue is known to have a nice property, the so-called insensitivity. In this paper, we generalize this for a single node queue with Poisson arrivals and background state, which changes at completion instants of lifetimes as well as at the arrival and departure instants. We study this problem by using the decomposability property of the joint stationary distribution of the queue length and supplementary variables, which implies the insensitivity. We formulate a Markov process representing the state of the queue as an RGSMP (reallocatable generalized semi-Markov process), and give necessary and sufficient conditions for the decomposability. We then establish general criteria to be sufficient for the queue to possess the property. Various symmetric-like queues with background states, including continuous time versions of moving server queues, are shown to have the decomposability.

Light-traffic in a cellular system with mobile subscribers and its applications

Abstract This paper is concerned with a cellular system with mobile subscribers (customers). This system consists of a cell, called the tagged cell, and its adjacent cells. Each cell has some finite number of channels. The sojourn times of customers in the tagged cell have an exponential distribution. Customers in the adjacent cells move to the tagged cell according to a Poisson process whose rate depends on the number of customers in the tagged cell. Each customer without call in progress generates his call according to an exponential distribution and the channel holding times of calls at each cell have a common exponential distribution. We first show that under some restriction, the light traffic limit for the stationary state distribution in the tagged cell is given by a mixture of a Poisson and binominal distributions. Based on the limit, we develop formulae for evaluating the hand-off and blocking probabilities and the mean number of busy channels in the tagged cell. Several numerical examples are presented that demonstrate the practical usefulness of the formulae.

Relationships in stationary jump processes with countable state space and their applications to queues

Abstract We consider a stationary continuous time process with a finite or countable state space, which is usually called a stationary pure jump process because it changes its state by jumps. Relationships between the stationary distributions at an arbitrary time, just before and after jump instants are obtained by using conditional sojourn times in states and in sets of states. For a skip free process, these distributions have product form expressions in terms of the conditional mean sojourn times. The results are applied to queueing models. We extend some known relationships between queueing characteristics to batch arrival and batch serve queues with stationary inputs. They also give a unified approach for truncation expressions for finite queues.

Guidelines for Design and Performance Evaluation of Production Lines Having Variable Operation Times and Limited in-Process Inventory

Recently, flexible manufacturing systems (FMs) have been recognized as one of the most important pieces of technology in computerized manufacturing.

QUASI-PRODUCT FORM TO A MULTINODE QUEUEING SYSTEM WITH A COMMON EXPONENTIAL SETUP SERVER

We consider a K-node queueing system sharing a setup server. Each node has a node server, a waiting position, and a service position, and it behaves as an M/G/1/2 type queue except that each job in the waiting position requires a setup by the setup server to move to the service position. The service discipline of the setup server is nonpreemptive work-conserving random selection. The setup times have a common exponential distribution. The main purpose of this paper is to derive the stationary distribution for the K-node system. For each node, we construct a corresponding setup server queue (CSQ). The stationary distribution of the K-node system is given by a product form of the stationary distributions of CSQs. This result enables us to obtain the stationary distribution of a K-node system by analyzing individual CSQs.