Dynamic admission and service rate control of a queue

Adusumilli, Kranthi Mitra; Hasenbein, John J.

doi:10.1007/s11134-010-9192-z

Cited by 43 publications

(20 citation statements)

References 10 publications

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“…The algorithm extends the work of Adusumilli and Hasenbein [2], who consider a problem in which there is both admission control and service rate control, from a single server setting with no customer abandonment to a many-server setting with customer abandonment. There is a rich history to their problem, but their motivation mainly comes from the work of George and Harrison [12], who consider a single server queue with service rate control, but leave open the problem of also including admission control.…”

Section: Literature Reviewmentioning

confidence: 91%

“…Hence y n 1 (2) > y n 2 (2). Continued iteration of the last two sentences shows y n 1 (k) > y n 2 (k) for k ∈ {1, .…”

Section: Proof Of Lemma 31 It Follows From (34) Thatmentioning

confidence: 94%

“…A threshold policy with threshold level l has θ(x) = 0 for all x < l and θ(x) = 1 for all x ≥ l. Any policy within the class of deterministic stationary policies is equivalent to a threshold policy when the system starts empty. 2 The threshold level l is exactly the smallest state in which customers are rejected. When the threshold level is finite, the system dynamics are equivalent to a M/M/N + M queueing model with a finite buffer, of size determined by the threshold level.…”

Section: The Admission Control Modelmentioning

confidence: 99%

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Admission control for a multi-server queue with abandonment

Koçağa

Ward

2010

Queueing Syst

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In a M/M/N + M queue, when there are many customers waiting, it may be preferable to reject a new arrival rather than risk that arrival later abandoning without receiving service. On the other hand, rejecting new arrivals increases the percentage of time servers are idle, which also may not be desirable. We address these trade-offs by considering an admission control problem for a M/M/N + M queue when there are costs associated with customer abandonment, server idleness, and turning away customers. First, we formulate the relevant Markov decision process (MDP), show that the optimal policy is of threshold form, and provide a simple and efficient iterative algorithm that does not presuppose a bounded state space to compute the minimum infinite horizon expected average cost and associated threshold level. Under certain conditions we can guarantee that the algorithm provides an exact optimal solution when it stops; otherwise, the algorithm stops when a provided bound on the optimality gap is reached. Next, we solve the approximating diffusion control problem (DCP) that arises in the Halfin-Whitt many-server limit regime. This allows us to establish that the parameter space has a sharp division. Specifically, there is an optimal solution with a finite threshold level when the cost of an abandonment exceeds the cost of rejecting a customer; otherwise, there is an optimal solution that exercises no control. This analysis also yields a convenient analytic expression for the infinite horizon expected average cost as a function of the threshold level. Finally, we propose a policy for the original system that is based on the DCP solution, and show that this policy is asymptotically optimal. Our extensive numerical study shows that the control that arises from solving the DCP achieves a very similar cost to the control that arises from solving the MDP, even when the number of servers is small.

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Section: Literature Reviewmentioning

confidence: 91%

“…Hence y n 1 (2) > y n 2 (2). Continued iteration of the last two sentences shows y n 1 (k) > y n 2 (k) for k ∈ {1, .…”

Section: Proof Of Lemma 31 It Follows From (34) Thatmentioning

confidence: 94%

Section: The Admission Control Modelmentioning

confidence: 99%

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Admission control for a multi-server queue with abandonment

Koçağa

Ward

2010

Queueing Syst

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“…비교 적 최근 Choi et al [12] 은 도착과정을 MMPP (Markovian [5] , Yoon and Lewis [7] 그리고 Adusumilli and Hasenbein [13] 등을 참고 해볼 수 있다. 마코프 의사결정과정이 아닌 본 연구와 유 사한 모델링 방식의 최근 연구는 Choi et al [14] 에서 찾아 볼 수 있다.…”

Section: 한국시뮬레이션학회 논문지unclassified

Analysis of an M/G/1/K Queueing System with Queue-Length Dependent Service and Arrival Rates

Choi¹,

Lim²

2015

Journal of the Korea Society for Simulation

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We analyze an  queueing system with queue-length dependent service and arrival rates. There are a single server and a buffer with finite capacity  including a customer in service. The customers are served by a first-come-first-service basis. We put two thresholds   and   ≧    on the buffer. If the queue length at the service initiation epoch is less than the threshold   , the service time of customers follows   with a mean of   and the arrival of customers follows a Poisson process with a rate of   . When the queue length at the service initiation epoch is equal to or greater than   and less than   , the service time is changed to   with a mean of   ≧    . The arrival rate is still   . Finally, if the queue length at the service initiation epoch is greater than   , the arrival rate of customers are also changed to a value of   ≦    and the mean of the service times is   . By using the embedded Markov chain method, we derive queue length distribution at departure epochs. We also obtain the queue length distribution at an arbitrary time by the supplementary variable method. Finally, performance measures such as loss probability and mean waiting time are presented.

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“…Although the model considered by Adusumilli and Hasenbein (2010) can be seen as more general than ours since they assume a continuum action set for service decisions, our simpler setting contributes to the research area in several ways. First, we analyze the discounted expected profit maximization in the infinite horizon and show that the optimal policy converges to the corresponding long run average optimal policy, under easily verifiable sufficient conditions on the cost functions.…”

Section: Introductionmentioning

confidence: 99%

The value of service rate flexibility in an M/M/1 queue with admission control

Dimitrakopoulos

Burnetas

2017

IISE Transactions

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We consider a single server queueing system with admission control and the possibility to switch dynamically between k increasing service rate values with service cost rate being convex in service rate. We explore the benefit due to service rate flexibility on the optimal profit and the admission thresholds, when service payment is made upon customer's admission. We formulate a Markov Decision Process model for the problem of joint admission and service control considering both discounted and average expected profit maximization, and show that the optimal policy has a threshold structure for both controls. Regarding the benefit due to flexibility, we show that it is increasing in system congestion, and that its effect on the admission policy is to increase the admission threshold. We also derive a simple approximate condition between the admission reward and the relative cost of service rate increase, so that the service rate flexibility is beneficial. We finally show that the results extend to the corresponding model where service payment is made at the end of each service completion and differences on the benefit due to service flexibility with respect to the original model are pursued numerically.

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Dynamic admission and service rate control of a queue

Cited by 43 publications

References 10 publications

Admission control for a multi-server queue with abandonment

Admission control for a multi-server queue with abandonment

Analysis of an M/G/1/K Queueing System with Queue-Length Dependent Service and Arrival Rates

The value of service rate flexibility in an M/M/1 queue with admission control

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