911 research outputs found

    Optimal Supply & Demand Balance In Service Environments

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    We study service environments that can be modeled as stochastic finite-capacity double-ended queues, where supply and demand arrive in independent Poisson processes to be instantly paired-off. In the case where throughput (output rate) is not a significant metric of system performance (as typically studied in the literature), we derive analytical results to gain managerial insights. We find that the operational decision on optimal supply/demand balance and the strategic decision on how to achieve that optimal balance can be decoupled and stratified. With the purpose of providing a managerial guide, we identify conditions for when to manipulate demand rather than supply, and vice versa. For the first time in the literature, we study throughput considerations in this context, and we analytically characterize the optimal strategy. Specifically, we show that it is optimal to manipulate either demand, or supply (and not both), and that the optimal system balance and the strategy on how to achieve it are strongly tied. Our findings can shed light on the managerial decision making process in these environments, and they can be used to revisit any governing strategies dictating management of demand (or supply) as a first course of action

    Diffusion Models for Double-ended Queues with Renewal Arrival Processes

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    We study a double-ended queue where buyers and sellers arrive to conduct trades. When there is a pair of buyer and seller in the system, they immediately transact a trade and leave. Thus there cannot be non-zero number of buyers and sellers simultaneously in the system. We assume that sellers and buyers arrive at the system according to independent renewal processes, and they would leave the system after independent exponential patience times. We establish fluid and diffusion approximations for the queue length process under a suitable asymptotic regime. The fluid limit is the solution of an ordinary differential equation, and the diffusion limit is a time-inhomogeneous asymmetric Ornstein-Uhlenbeck process (O-U process). A heavy traffic analysis is also developed, and the diffusion limit in the stronger heavy traffic regime is a time-homogeneous asymmetric O-U process. The limiting distributions of both diffusion limits are obtained. We also show the interchange of the heavy traffic and steady state limits

    Balancing Queueing Systems With Excess Demand

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    In a rough economic environment and increased competition, one issue critical to many businesses is to achieve an optimum balance between supply and demand. Double-ended queuing structure, where demand and supply occur simultaneously, can be utilized to model various manufacturing and service activities. By associating costs per time unit due to a unit of excess of supply or demand, the total cost will include now costs due to imbalance of demand and supply. The authors examine the queuing behavior and how to minimize the above total cost by advanced planning aimed to hold imbalance costs at a minimum.In this paper, the main focus will be on situations where a stochastic system has become unstable due to demand exceeding supply. To determine how sensitive optimal solutions are to changes in model parameters, for each policy, either decreasing demand or increasing supply, exact optimal solutions were found for a large number of scenarios and then used this scenarios database to fit the best possible regression model. The paper ends illustrating the use of the model to research funding where typically proposals compete for scarce funding resources

    Queuing Models To Balance Systems With Excess Supply

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    Many manufacturing and service activities can be modeled using queuing theory. The optimization of the long-run solution to imbalances between supply and demand is very important to established businesses. This paper presents a family of queuing models that minimize the expected total cost incurred when restoring equilibrium to a stochastic system that has become unstable due to changes in the environmental parameters affecting its behavior. Analytical expressions for the expected total cost in terms of a policy parameter are derived from which numerically-savvy users can obtain the policy that minimizes the expected total cost. To determine the model parameters that most affect the optimal policy and to facilitate the determination of near-optimal policies, exact solutions were found for a large number of scenarios and then used to fit a regression model. The resulting regression equation can be used by practitioners to find policy parameters that approximately minimize the expected total cost due to imbalances in supply and demand

    Operations management for double-ended queues

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    In this paper we have presented the double-ended queueing model with its generic form, abstract modeling extensions, different types of controls to be assumed by the management of the system, as well as optimization via various methodologies. Since its inception in 1950s, double-ended queuing model has had widespread use and recently it is observed that literature is focusing on social welfare perspectives on queues under strategically acting customers and enhanced information exchange due to advanced technology. It is also reviewed that for the complex and analytically tractable versions of double-ended queues it is possible to obtain approximate or near-optimal results via methodologies such as simulation and fluid and diffusion approximations.No sponso

    A double-ended queue with catastrophes and repairs, and a jump-diffusion approximation

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    Consider a system performing a continuous-time random walk on the integers, subject to catastrophes occurring at constant rate, and followed by exponentially-distributed repair times. After any repair the system starts anew from state zero. We study both the transient and steady-state probability laws of the stochastic process that describes the state of the system. We then derive a heavy-traffic approximation to the model that yields a jump-diffusion process. The latter is equivalent to a Wiener process subject to randomly occurring jumps, whose probability law is obtained. The goodness of the approximation is finally discussed.Comment: 18 pages, 5 figures, paper accepted by "Methodology and Computing in Applied Probability", the final publication is available at http://www.springerlink.co
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