This paper presents a new nonlinear mathematical model to solve a cell formation problem which assumes that processing time and inter-arrival time of parts are random variables. In this research, cells are defined as a queue system which will be optimized via queuing theory. In this queue system, each machine is assumed as a server and each part as a customer. The grouping of machines and parts...

Motivated by applications in computer networks, in this talk, we consider a tandem queue with feedback.In this model, both the interarrival time and the service time are exponential. Upon completion of the service at thesecond station, the customer either leaves the system with probability p or goes back together with all customersin the second queue to the first queue with probabil...

We consider the problem of forming a distributed queue in the adversarial dynamic network model of Kuhn, Lynch, and Oshman (STOC 2010) in which the network topology changes from round to round but the network stays connected. This is a synchronous model in which network nodes are assumed to be fixed, the communication links for each round are chosen by an adversary, and nodes do not know who th...

We consider a system of parallel queues with dedicated arrival streams. At each decision epoch a decisionmaker can move customers from one queue to another. The cost for moving customers consists of a fixed cost and a linear, variable cost dependent on the number of customers moved. There are also linear holding costs that may depend on the queue in which customers are stored. Under very mild a...

Analytical models for IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known decoupling approximation proposed by Bianchi for modeling single cell WLANs consisting of saturated nodes. In this paper, we provide a new approach to model the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model M queues (one...

In this paper we study a MAP/M/K system with join-the-shortest-queue (JSQ) discipline which consists of K servers and K queues with infinite buffers. An arrival joins the shortest queue and in the case that there are n (n≤ K) queues having the same shortest length, the customer will join any one of these shortest queues with probability 1/n. We model the system as a levelexpanding QBD (LDQBD) p...

We consider a system of two parallel queues sharing a common arrival process, where the arriving customers select which queue to join based on a generalized Join the Shortest Queue ( ) policy. We assume that both servers run at the same speed. However, we assume that departing customers face some additional delay after leaving the system, and that this downstream delay is different between the ...

In this paper, we consider a system modelled as an M/M/1 queue. Several users send jobs to the queue and are characterized by a delay cost per unit of time and a demand function. Our goal is to design an optimal pricing scheme for the queue, where the total charge depends on both the mean delay at the queue and arrival rate of each customer. We also assume that those two values have to be (stat...

People tend to lack the self control to undergo an unpleasant service that would generate future bene…ts. This paper derives a tractable quasi-hyperbolic discounting model of that behavioral tendency (for queueing systems in which service time is short relative to the time horizon for its bene…ts, and customers observe the queue). People’s lack of self control makes it socially optimal to hide ...

The Internet routers employing the random early detection (RED) algorithm for congestion control suffer from the problem of chaotic queue oscillation. It is well known that the slowly varying nature of the average queue size computed using an exponentially weighted moving average (EWMA) used in the RED scheme causes this chaotic behavior. This paper presents a new mathematical function to model...