Optimal use of excess capacity in two interconnected queues

Pandelis, Dimitrios G.

doi:10.1007/s00186-006-0112-2

Cited by 12 publications

(20 citation statements)

References 14 publications

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“…From Eqs. (16), (17), and (11), we obtain (25) because d(0, x 2 ) < 0 (Lemma 1) and ν 1 ≥ μ 1 . Therefore, d(1, 0) > d (1,1).…”

Section: Proof Of Lemmamentioning

confidence: 87%

“…With the exception of Pandelis [16] (constrained version), a common assumption in all the papers referred to in the previous paragraph was that different servers could collaborate to work on the same job, in which case the total service rate was equal to the sum of the individual servers rates. Moreover, a nonidling discipline for at least the dedicated servers was assumed in all of these papers.…”

Section: Introductionmentioning

confidence: 99%

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Optimal control of noncollaborative servers in two‐stage tandem queueing systems

Pandelis¹

2014

Naval Research Logistics

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We consider two‐stage tandem queueing systems with dedicated servers in each station and a flexible server that is trained to serve both stations. We assume no arrivals, exponential service times, and linear holding costs for jobs present in the system. We study the optimal dynamic assignment of servers to jobs assuming a noncollaborative work discipline with idling and preemptions allowed. For larger holding costs in the first station, we show that (i) nonidling policies are optimal and (ii) if the flexible server is not faster than the dedicated servers, the optimal server allocation strategy has a threshold‐type structure. For all other cases, we provide numerical results that support the optimality of threshold‐type policies. Our numerical experiments also indicate that when the flexible server is faster than the dedicated server of the second station, the optimal policy may have counterintuitive properties, which is not the case when a collaborative service discipline is assumed. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 435–446, 2014

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“…From Eqs. (16), (17), and (11), we obtain (25) because d(0, x 2 ) < 0 (Lemma 1) and ν 1 ≥ μ 1 . Therefore, d(1, 0) > d (1,1).…”

Section: Proof Of Lemmamentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Optimal control of noncollaborative servers in two‐stage tandem queueing systems

Pandelis¹

2014

Naval Research Logistics

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“…Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Pandelis [17] showed the validity of the results obtained by Farrar [8,9] for the case when jobs might leave the system after D. G. Pandelis Andradottir, Ayhan,, Gel, Hopp, and Van Oyen [10,11], Hopp, Tekin, and Van Oyen [12], Iravani, Van Oyen, and Sims [15], and Ahn and Righter [3].…”

mentioning

confidence: 78%

Optimal Control of Flexible Servers in Two Tandem Queues With Operating Costs

Pandelis¹

2007

Prob. Eng. Inf. Sci.

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We consider two-stage tandem queuing systems with dedicated servers in each station and flexible servers that can serve in both stations. We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Moreover, we present conditions under which the optimal policy can be explicitly determined. Andradottir, Ayhan,, Gel, Hopp, and Van Oyen [10,11], Hopp, Tekin, and Van Oyen [12], Iravani, Van Oyen, and Sims [15], and Ahn and Righter [3]. These models include collaborative and noncollaborative work disciplines, open systems with external arrivals that are independent of the system state, closed systems (e.g., CONWIP systems where a departure triggers a new arrival), and various forms of cross-training (e.g., full, zone, or hierarchical cross-training).There is also much research on the optimal use of flexible servers in tandem systems with holding costs. Because the mathematical models involved are quite complex, most results refer to two-stage systems and exponential service times. Rosberg, Varaiya, and Walrand [19] considered a system with Poisson arrivals, a server with a constant service rate in the downstream station, and a server with a controllable service rate in the upstream station. They showed that the optimal service rate is nondecreasing in the length of the first queue and nonincreasing in the length of the second queue. Weber and Stidham [23] considered a system of n stations with arrivals at each station, where, in addition to convex holding costs, servers incur operating costs that are convex functions of their service rates. They showed that the optimal policy is transition-monotone; that is, when a job leaves a queue, the optimal service rate in that queue is not increased and the optimal service rates in the other queues are not decreased. Duenyas, Gupta, and Olsen [7] and Iravani, Posner, and Buzacott [14] characterized optimal policies for models of n and two-stage systems, respectively, with one flexible server and setup costs. Pandelis and Teneketzis [18] studied two-stage clearing systems with multiple flexible servers where jobs join the second queue with probability p after completing service in the upstream station. They derived conditions under which the policy that gives priority to jobs in the upstream station is optimal for general service times. For a two-stage clearing system with two flexible servers, Ahn, Duenyas, and Zhang [2] provided necessary and sufficient conditions under which an exhaustive policy for the upstream or the downstream station is optimal. Similar results were obtained by Ahn, Duenyas, and Lewis [1] for the model with arrivals. The results of Ahn et al. [2] have been extended in two more directions. First, Schiefermayr and Weichbold [20] obtained the optimal policy for all values of holding costs and service times. Se...

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“…The use of floaters in clearing systems (no external arrival of jobs until originally scheduled jobs clear) has been well studied [46][47][48][49]. Particularly, dynamic allocation of floaters in clearing systems of two tandem queues have been modeled as DP problems.…”

Section: Floatersmentioning

confidence: 99%

“…Three optimal policies were derived for different conditions, which include (i) an exhaustive policy for job type-2, (ii) a non-increasing boundary in the queue of job type-1, and (iii) a non-decreasing boundary in the queue of job type-1. Pandelis [49] extended these models and considered conditions of jobs leaving the system after leaving the first station, as well as less constrained cases where the floater can work on both stations. Pandelis [46] later considered the operating cost of using floaters, finding that it may be optimal to idle the floater when the operating costs are higher than holding costs.…”

Section: Floatersmentioning

confidence: 99%