Search

The so called “Israeli Queue” is a single server polling system with batch service of an unlimited size, where the next queue to be visited is the one in which the first customer in line has been waiting for the longest time. The case with finite number of queues (groups) was introduced by Boxma, Van der Wal and Yechiali [3]. In this paper we extend the model to the case with a (possibly) infinite number of queues. We analyze the M/M/1, M/M/c, and M/M/1/N—type queues, as well as a priority model with (at most) M high-priority classes and a single lower priority class. In all models we present an extensive probabilistic analysis and calculate key performance measures. [ABSTRACT FROM PUBLISHER]

Timers are used as a control mechanism to constrain the service periods in various telecommunication networks. In this paper we introduce and analyze a general family of timer-type models, called Randomly Timed Gated (RTG) queueing systems, which, in addition, extends and generalizes the family of M/G/1-type queues with server intermissions. The control mechanism is such that, whenever the server reenters the system, an exponential Timer T is activated. If the server empties the queue before the Timer's expiration, it immediately leaves for another intermission. Otherwise (if the Timer expires when there is still work in the system), the server obeys one of the following rules, each leading to a different model: (1) The server completes all the work accumulated up to time T, and leaves. (2) The server completes only the service of the job currently being served, and leaves. (3) The server leaves immediately. Consequently, the CRT queue forms a unified structure for a vast collection of timer-type models: Under rule (1) it spans an entire spectrum of regimes lying between the Gated and the Exhaustive. Under rule (2) it spans an entire spectrum between the 1-Limited and the Exhaustive disciplines. The analysis is achieved through a general solution of an infinite set of linear equations where the unknowns are the state-dependent joint transforms of two key characteristics: the length of a busy period starting with r jobs (r = 0, 1, 2,...), and the number of jobs left behind at the end of such a busy period. We show that, in steady state, a complete description of the CRT system can be obtained explicitly in terms of the probability generating function (PGF) of the queue size at a start of a busy period. A fixed point equation for this PGF can be constructed when the structure of the intermission interval is specified. We derive various performance measures for the three models in steady state. [ABSTRACT FROM AUTHOR]

Accelerating procedures for solving discounted Markov decision processes problems are developed based on a one-step lookahead analysis of the value iteration algorithm. We apply the criteria of minimum difference and minimum variance to obtain good adaptive relaxation factors that speed up the convergence of the algorithm. Several problems (including Howard's automobile replacement) are tested and a preliminary numerical evaluation reveals considerable reductions in computation time when compared to existing value iteration schemes. [ABSTRACT FROM AUTHOR]

Studies a single-server queue with Poisson arrivals and multiple customer feedbacks. Description of the gated vacation strategy; Joint queue length process of new and old customers; Waiting time distribution of customers.

Copyright of INFOR is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We study the behavior of a single-server discrete-time queue with batch arrivals, where the information on the queue length and possibly on service completions is delayed. Such a model describes situations arising in high speed telecommunication systems, where information arrives in messages, each comprising a variable number of fixed-length packets, and it takes one unit of time (a slot) to transmit a packet. Since it is not desirable to attempt service when the system may be empty, we study a model where we assume that service is attempted only if, given the information available to the server, it is certain that there are messages in the queue. We characterize the probability distribution of the number of messages in the queue under some general stationarity assumptions on the arrival process, when information on the queue size is delayed K slots, and derive explicit expressions of the PGF of the queue length for the case of i.i.d. batch arrivals and general independent service times. We further derive the PGF of the queue size when information on both the queue length and service completion is delayed K=1 units of time. Finally, we extend the results to priority queues and show that when all messages are of unit length, the cμ rule remains optimal even in the case of delayed information. [ABSTRACT FROM AUTHOR]

A double-space parking problem is studied for a parking lot of size M accommodating both private cars and buses. Upon arrival, a private car is either admitted to the parking lot, occupying a single spot, or waits in line until a spot becomes available. An arriving bus occupies double spots and is admitted only if there are at least two free spots. It balks from the system otherwise. The inflow is governed by two independent Poisson streams, with rates λ C for cars and λ B for buses. The sojourn time of a car or a bus inside the parking lot is exponentially distributed with parameters μ C and μ B , respectively. The problem is formulated as a QBD process and analyzed via matrix geometric methods. Various performance measures are calculated, including mean number of cars inside, and outside, the parking lot; mean number of buses in the system; and the probability that an arriving bus is blocked. The dichotomy whether to split the M-spot lot into two separate lots, one for cars, the other for buses, is studied and the optimal split is calculated. Numerical results are presented via graphs. Finally, it is shown that from the point of view of the parking lot owner, it is equivalent to either charge a fixed entrance fee or charge per-time unit of usage. [ABSTRACT FROM AUTHOR]

The article presents several letters to the editor in response to articles in previous issues, including one on the Shapley Value and another on a stochastic bottleneck assignment problem.