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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2009.02.024 Byline: Nir Perel (a), Uri Yechiali (a)(b) Keywords: Alternating queue; M / M / 1 ; M / M / c ; M / M / [infinity] ; Slow server(s); Impatient customers; Abandonment Abstract: We study M/M/c queues (c=1, 1 We concentrate on deriving analytic solutions to the queue-length distributions. We derive, for each case of c, the corresponding probability generating function, and calculate the mean queue size. Several extreme cases are investigated and numerical results are presented. Author Affiliation: (a) Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel (b) Afeka Academic College of Engineering, Afeka, Tel Aviv 69107, Israel Article History: Received 6 August 2008; Accepted 18 February 2009

The effect of breakdown and repairs on polling systems is analyzed. The repairs are considered in three service mechanisms: Gated, Exhaustive and Globally Gated.

A look-ahead method for Value Iteration Algorithms used in solving both discounted and undiscounted Markov decision processes is presented. Based on the value-oriented concept which incorporates multiple adaptive relaxation factors, the approach leads to procedures which perform better than the separate application of either the concept of value oriented or of relaxation. The approach also appears useful in solving large-scale Markov decision processes.

The risk of infection from the COVID-19 virus dictates businesses, such as supermarkets and department stores, to impose limits on the maximal number of customers allowed inside a store at any given time. These social distancing constraints generate long queues of waiting customers outside such businesses. This work investigates the impact of infection risk on arriving customers' strategic decisions regarding joining such queues. We consider a typical store where the floor is divided into two separate areas: (i) a shopping area with at most K shoppers allowed, and (ii) a payment area with c ≥ 1 parallel servers and an adjacent limited waiting space of size N ≥ 0. When the shopping area is full, a newly arriving customer observes only the outside queue and decides whether to join or balk. We investigate customers' individual joining strategies, as well as social optimization, with a utility function that takes into account not only the cost associated with waiting times (as in Naor's (1969) celebrated model), but also the cost related to the risk of infection. We propose an innovative risk measure that is a function of both the number of customers already in line, and those that a tagged customer 'meets' while waiting to enter the store. Consequently, expressions for mean waiting times and infection risk are derived and explicit formulas are obtained for limit values of the parameters. Our results can be used by authorities and customers alike to determine the maximal allowed queue sizes that ensure safety and reduce the risk of infection while minimizing associated costs. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has forced numerous businesses such as department stores and supermarkets to limit the number of shoppers inside the store at any given time to minimize infection rates. We construct and analyze two models designed to optimize queue sizes and customer waiting times to ensure safety. In both models, customers arrive randomly at the store and, after receiving permission to enter, pass through two service phases: shopping and payment. Each customer spends a random period of time shopping (first phase) and then proceeds to the payment area of the store (second phase) where cashiers are assigned to serve customers. We propose a novel approach by which to calculate the risk of a customer being infected while queueing outside the store, while shopping, and while checking out with a cashier. The risk is proportional to the second factorial moment of the number of customers occupying the space in each phase of the shopping route. We derive equilibrium strategies for a Stackelberg game in which the authority acts as a leader who first chooses the maximum number of customers allowed inside the store to minimize the risk of infection. In the first model, store' management chooses the number of cashiers to provide to minimize its operational costs and its customers' implied waiting costs based on the number allowed in the store. In the second model, the store partitions its total space into two separate areas – one for shoppers and one for the cashiers and payers – to increase cashiers' safety. Our findings and analysis are useful and applicable for authorities and businesses alike in their efforts to protect both customers and employees while reducing associated costs. [ABSTRACT FROM AUTHOR]

We propose a novel approach, based on a Human Leukocyte Antigen (HLA) best-fit criterion, to dynamically allocate live organs (specifically, kidneys) to candidates needing transplantation. A ‘reward’ is assigned to each level of HLA fit, such that higher rewards are attributed to transplants between better-matched candidates and kidneys. We also envision future technologies by which it will be possible to store organs so that two queues may form: waiting candidates or stored kidneys. Consequently, a double-ended queue of candidates and kidneys is constructed, where the lifetime of a stored kidney is random, and candidates queueing for transplantation may die (‘renege’) while waiting. We derive expressions for the probability that a candidate gets a kidney before reneging; for the mean numbers of waiting candidates and of stored kidneys; and for a candidate's or kidney's mean sojourn time. Assuming a best-HLA-fit matching policy, we study three measures of effectiveness: (i) Rate of Reward from Transplantation (RRT); (ii) Expected Reward per Transplantation (ERT), calculated as RRT divided by the rate of performed transplantations, and (iii) Gained rate of reward per one dollar of expenditure. The optimal fraction of kidneys that should be stored so as to maximize the rate of reward per one dollar of expenditure is numerically determined. [ABSTRACT FROM AUTHOR]

One of the main challenges facing biology today is the understanding of the joint action of genes, proteins and RNA molecules, interwoven in intricate interdependencies commonly known as genetic networks. To this end, several mathematical approaches have been introduced to date. In addition to developing the analytical tools required for this task anew, one can utilize knowledge found in existing disciplines, specializing in the representation and analysis of systems featuring similar aspects. We suggest queueing theory as a possible source of such knowledge. This discipline, which focuses on the study of workloads forming in a variety of scenarios, offers an assortment of tools allowing for the derivation of the statistical properties of the inspected systems. We argue that a proper adaptation of modeling techniques and analytical methods used in queueing theory can contribute to the study of genetic regulatory networks. This is demonstrated by presenting a queueing-inspired model of a genetic network of arbitrary size and structure, for which the probability distribution function is derived. This model is further applied to the description of the lac operon regulation mechanism. In addition, we discuss the possible benefits stemming for queueing theory from the interdisciplinary dialogue with molecular biology—in particular, the incorporation of various dynamical behaviours into queueing networks. [Copyright &y& Elsevier]

We study a single-server queue in which the service consists of two independent stages. The first stage is generic and can be performed even in the absence of customers, whereas the second requires the customer to be present. When the system is empty of customers, the server produces an inventory of first-stage (‘preliminary’) services (denoted PSs), which is used to reduce customers’ overall sojourn times. We formulate and analyze the queueing-inventory system and derive its steady-state probabilities by using the matrix geometric method, which is based on calculating the so called rate matrix R . It is shown that the system's stability is not affected by the production rate of PSs, and that there are cases in which utilizing the server's idle time to produce PSs actually increases the fraction of time during which the server is dormant. A significant contribution is the derivation of an explicit expression of R , whose entries are written in terms of Catalan numbers. This type of result is rare in the literature and enables large-scale problems to be solved with low computational effort. Furthermore, by utilizing Laplace–Stieltjes transform and its inverse, we obtain the distribution function of customers’ sojourn time. Finally, based on the probabilistic study, we carry out an economic analysis using a practical example from the fast food industry. [ABSTRACT FROM AUTHOR]