Papers by Mohammed BOUALEM
Mathematical Problems in Engineering, 2012
This paper focuses on stochastic comparison of the Markov chains to derive some qualitative appro... more This paper focuses on stochastic comparison of the Markov chains to derive some qualitative approximations for anM/G/1retrial queue with a Bernoulli feedback. The main objective is to use stochastic ordering techniques to establish various monotonicity results with respect to arrival rates, service time distributions, and retrial parameters.
Bulletin of the iranian mathematical society
We propose to use a mathematical method based on stochastic comparisons of Markov chains in order... more We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds. The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques.
Bulletin of The Iranian Mathematical Society, 2017
In this work, we derive insensitive bounds for various performance measures of a single-server... more In this work, we derive insensitive bounds for various performance measures of a single-server retrial queue with generally distributed inter-retrial times and Bernoulli schedule, under the special assumption that only the customer at the head of the orbit queue (i.e., a FCFS discipline governing the flow from the orbit to the server) is allowed to occupy the server. The methodology is strongly based on stochastic comparison techniques. Instead of studying a performance measure in a quantitative fashion, this approach attempts to reveal the relationship between the performance measures and the parameters of the system. We prove the monotonicity of the transition operator of the embedded Markov chain relative to strong stochastic ordering and increasing convex ordering. We obtain comparability conditions for the distribution of the number of customers in the system. Bounds are derived for the stationary distribution and some simple bounds for the mean cha...
Discrete and Continuous Models and Applied Computational Science
In this investigation, we consider an M/G/1 queue with general retrial times allowing balking and... more In this investigation, we consider an M/G/1 queue with general retrial times allowing balking and server subject to breakdowns and repairs. In addition, the customer whose service is interrupted can stay at the server waiting for repair or leave and return while the server is being repaired. The server is not allowed to begin service on other customers until the current customer has completed service, even if current customer is temporarily absent. This model has a potential application in various fields, such as in the cognitive radio network and the manufacturing systems, etc. The methodology is strongly based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary distribution of the embedded Markov chain of the considered system.
Hacettepe journal of mathematics and statistics, Oct 31, 2023
Consider a single-server retrial queueing system with non-preemptive priority service, where cust... more Consider a single-server retrial queueing system with non-preemptive priority service, where customers arrive in a Poisson process with a rate of λ 1 for high-priority customers (class 1) and λ 2 for low-priority customers (class 2). If a high-priority customer is blocked, they are queued, while a low-priority customer must leave the service area and return after some random period of time to try again. In contrast with existing literature, we assume different service time distributions for the two customer classes. This investigation proposes a stochastic comparison method based on the general theory of stochastic orders to obtain lower and upper bounds for the joint stationary distribution of the number of customers at departure epochs in the considered model. Specifically, we discuss the stochastic monotonicity of the embedded Markov queue-length process in terms of both the usual stochastic and convex orders. We also perform a numerical sensitivity analysis to study the effect of the arrival rate of high-priority customers on system performance measures.
Yugoslav Journal of Operations Research, 2019
In this article we analyze the M=G=1 retrial queue with two-way communication and n types of outg... more In this article we analyze the M=G=1 retrial queue with two-way communication and n types of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain that cannot be analyzed numerically, we propose to bound it by a new Markov chain, which is easier to solve by using a stochastic comparison approach. Particularly, we study the monotonicity of the transition operator of the embedded Markov chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the embedded Markov chain at departure epochs. Additionally, the performance measures of the considered system can be estimated by those of an M=M=1 retrial queue with two-way communication and n types of outgoing calls when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.
Hacettepe Journal of Mathematics and Statistics, 2018
The main goal in the present paper is to provide a technique that considers the stochastic compar... more The main goal in the present paper is to provide a technique that considers the stochastic comparison approach for investigating monotonicity and comparability of an M1, M2/G1, G2/1 retrial queues with two way communication. This approach is developed for comparing a non Markov process to Markov process with many possible stochastic orderings. Particularly, we show the monotonicity of the transition operator of the embedded Markov chain relative to the strong stochastic ordering and convex ordering, as well as the comparability of two transition operators. Bounds are also obtained for the stationary distribution of the number of customers at departure epochs. Additionally, the performance measures of the system considered can be estimated by those of an M1, M2/M1, M2/1 retrial queue with two way communication when the service time distribution is NBUE (respectively NWUE). Finally, we validate stochastic comparison results by presenting a numerical example illustrating the interest of the approach.
Quality Technology & Quantitative Management, 2018
This paper deals with a batch arrivals queue with general retrial time, breakdowns, repairs and r... more This paper deals with a batch arrivals queue with general retrial time, breakdowns, repairs and reserved time. Here we assume that customers arrive according to compound Poisson processes. Any arriving batch of primary customers finds the server free, one of the customers from the batch enters into the service area and the rest of them join into the orbit. The primary customers who find the server busy or failed are allowed to balk or are queued in the orbit in accordance with FCFS retrial policy. The customer whose service is interrupted can stay at the server waiting for repair or enter into service orbit. After the repair is completed, the server resumes service immediately if the customer in service has remained in the service position. This model has a potential applications in various fields, such as in the cognitive radio network and the manufacturing systems. By using supplementary variables technique, we carry out an extensive analysis of the considered model. Then, we obtain some important performance measures, stochastic decomposition property of the system size distribution and the reliability indices. Next, by setting the appropriate parameters, some special cases are discussed. Finally, some numerical examples and cost analysis are presented.
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Papers by Mohammed BOUALEM