Optimal priorities in GI|Gn|1 queue

A polynomial-time algorithm based on reduction to a polyhedron minimization problem is proposed for minimizing a given function F(W₁,...,W_n) that depends on the mean waiting times in the Gl|G_n|l queue.Translated from Kibernetika, No. 2, pp. 80–85, March–April, 1991.     

The GI/M/1 queue and the GI/Geo/1 queue both with single working vacation

We first consider the continuous-time GI/M/1 queue with single working vacation (SWV). During the SWV, the server works at a different rate rather than completely stopping working. We derive the steady-state distributions for the number of customers in the system both at arrival and arbitrary epochs, and for the FIFO sojourn time for an arbitrary customer. We then consider the discrete-time GI/Geo/1/SWV queue by contrasting it with the GI/M/1/SWV queue.     

Control of M|M|1|N queue parameters under constraints

An optimal control of the MM1N queue is considered on the basis of the minimum criterion for the expected service time if constraints on the average number of rejected demands and average energy expenditure are present. Two variants of an input flow are studied: with the separation of demands according to priorities and without such a separation. A dual optimization method and a Lagrange multiplier rule are used to synthesize a constrained optimal control. Two iteration procedures, the effectiveness of which is analyzed on the basis of the numerical simulation results, are presented in order to solve numerically a dual problem.     

On asymptotics of the emptiness probability in the M/GI/1 queue

We obtain the asymptotic estimation for the non-stationary emptiness probability in the M/GI/1 queue for the case of regularly varying tails of service-time distribution.     

Analytic and computational analysis of the discrete-time GI/D-MSP/1 queue using roots

This paper presents a simple closed-form analysis for evaluating system-length distributions at various epochs of the discrete-time GI/D-MSP/1 queue. The proposed analysis is based on roots of the associated characteristic equation of the vector-generating function of system-length distribution at prearrival epochs. We provide the steady-state system-length distribution at random epoch by using the classical argument based on Markov renewal theory. The queueing-time distribution has also been investigated. Numerical aspects have been tested for a variety of interarrival- and service-time distributions and a sample of numerical outputs is presented.     

A note on varying the number of states in the arrival process of MR/GI/1 queue

A single server queue with an autocorrelated arrival process is considered. A specific way of changing the number of states in the arrival process is introduced which enables us to extract the pure effect of the number of different types of arrivals on the queueing performance measures. We see that increasing the number of arrival types makes the arrival stream more correlated and causes longer waiting times in the system. This impact is much stronger when the successive arrival types tends to be the same under heavy traffic.     

Steady state analysis of the GI/M/1/N queue with a variant of multiple working vacations

This paper studies the GI/M/1/N queue with a variant of multiple working vacations, where the server leaves for a working vacation as soon as the system becomes empty. The server takes at most H consecutive working vacations if the system remains empty after the end of a working vacation. Employing the supplementary variable and embedded Markov chain methods, we obtain the queue length distribution at different time epochs. Based on the various system length distribution, the probability of blocking, mean waiting times and mean system lengths have been derived. Finally, numerical results are discussed.     

Moments of the queue size distribution in the MAP/G/1 retrial queue

We consider an MAP/G/1 retrial queue. A necessary and sufficient condition is obtained for the existence of the moments of the queue size distribution. The condition is expressed in terms of the moment condition for a service time distribution. In addition, we provide recursive formulas for the moments of the queue size distribution. Numerical examples are given to illustrate our results.     

A formalization of absolute and relative dates based on the point calculus

In this paper we present a formalization of absolute and relative dates based on a formalization of the point calculus. We discuss three extensions of the point calculus, namely absolute dates, relative dates and both kinds of dates. An approach to translate the point calculus with relative dates to a tense logic is suggested.     

Stochastic complexity for mixture of exponential families in generalized variational Bayes

The Variational Bayesian learning, proposed as an approximation of the Bayesian learning, has provided computational tractability and good generalization performance in many applications. However, little has been done to investigate its theoretical properties.     

Performance evaluation of CAI and RAI transmission modes in a GI-G-1 queue

In this paper, a discrete-time single-server queue is considered with an uncorrelated message arrival process and an uncorrelated server interruption process. The length of the messages is modeled as a series of positive i.i.d. random variables and two operation modes are considered. In continue after interruption mode (CAI) the processing of an interrupted message resumes with the next packet of this message. In repeat after interruption mode (RAI), the complete message is reprocessed after a server interruption. Using a generating-functions approach, explicit expressions for the mean and variance of buffer occupancy and message delay are derived for both operation modes. For illustration purposes, a discrete-time Pois-Geo-1 system is then evaluated.Scope and purposeDiscrete-time queueing theory has gained a lot of interest recently to describe queueing related phenomena in an environment where time is slotted, such as various digital computer and communication systems including mobile and B-ISDN networks based on asynchronous transfer mode technology. This work focuses on a discrete-time queueing system with server interruptions, which can occur when several users have to share a common resource, or when this resource is temporarily unavailable due to external causes such as maintenance or system failures. The contribution of this paper mainly lies in the model that is considered, the solution method that is applied, as well as the results that are generated. First, we want to introduce a model with an interrupted service process that allows us to compare an environment where interrupted messages must be retransmitted with the situation where this is not the case. Second, we will show that a generating-functions approach is extremely suitable for solving such a queueing model. And finally, we want to establish closed-form formulas in terms of the system parameters that enable us to assess the system performance for the two transmission modes that are considered.     

On three concepts in robust design optimization: absolute robustness,relative robustness,and less variance

Structural and Multidisciplinary Optimization - This paper provides a clear perspective on existing several different approaches to robust design optimization of structures. We primarily consider...     

Asymptotic analysis and simple approximation of the loss probability of the GI/M/c/K queue

We consider the GI^X/M/c/K queues with partial rejection or total rejection, and find an asymptotic behavior of loss probability of the GI^X/M/c/K queue as K tends to infinity. The asymptotic loss probability is expressed only in terms of the roots of the characteristic equation and the boundary probabilities of the corresponding GI^X/M/c queue. Numerical examples show that the asymptotic loss probability is a quite accurate approximation for the loss probability of the GI^X/M/c/K queue even when the system capacity K is moderate.     

Perturbation analysis of waiting times in the G/G/1 queue

This paper is devoted to perturbation analysis of the stationary distribution of waiting times in the G/G/1 queue with a parameter-dependent service time distribution. We provide sufficient conditions under which the stationary distribution is Lipschitz continuous and we explicitly compute the Lipschitz constant. Thereby, we provide bounds on the effect of a (finite) perturbation of the service time distribution on the stationary waiting time. The case of infinitesimal perturbations (read, derivatives) is treated as well.     

Asymptotic Analysis of an Retrial Queueing System M|M|1 with Collisions and Impatient Calls

We consider a single-line RQ-system with collisions with Poisson arrival process; the servicing time and time delay of calls on the orbit have exponential distribution laws. Each call in orbit has the “impatience” property, that is, it can leave the system after a random time. The problem is to find the stationary distribution of the number of calls on the orbit in the system under consideration. We construct Kolmogorov equations for the distribution of state probabilities in the system in steady-state mode. To find the final probabilities, we propose a numerical algorithm and an asymptotic analysis method under the assumption of a long delay and high patience of calls in orbit. We show that the number of calls in orbit is asymptotically normal. Based on this numerical analysis, we determine the range of applicability of our asymptotic results.     

A MAP|G|1|n System of Inverse Service Discipline and Resumption of Service of an Interrupted Customer with His Initial Duration

Stationary probabilities of the states of a single-server system with Markov input flow, inverse service discipline, and interruption are determined under the assumption that the interrupted customer is served anew with his initial service duration.