Constrained admission control to a queueing system

Arie Hordijk; Flos Spieksma

doi:10.2307/1427167

Constrained admission control to a queueing system

Advances in Applied Probability ◽

10.1017/s0001867800018619 ◽

1989 ◽

Vol 21 (02) ◽

pp. 409-431 ◽

Cited By ~ 5

Author(s):

Arie Hordijk ◽

Flos Spieksma

Keyword(s):

Mathematical Model ◽

Cost Function ◽

Admission Control ◽

Optimal Policy ◽

Efficient Algorithm ◽

Queueing System ◽

Markov Decision ◽

Service Rates ◽

Good Policy ◽

Proper Balance

We consider an exponential queue with arrival and service rates depending on the number of jobs present in the queue. The queueing system is controlled by restricting arrivals. Typically, a good policy should provide a proper balance between throughput and congestion. A mathematical model for computing such a policy is a Markov decision chain with rewards and a constrained cost function. We give general conditions on the reward and cost function which guarantee the existence of an optimal threshold or thinning policy. An efficient algorithm for computing an optimal policy is constructed.

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Bias optimal admission control policies for a multiclass nonstationary queueing system

Journal of Applied Probability ◽

10.1017/s0021900200021483 ◽

2002 ◽

Vol 39 (01) ◽

pp. 20-37 ◽

Cited By ~ 8

Author(s):

Mark E. Lewis ◽

Hayriye Ayhan ◽

Robert D. Foley

Keyword(s):

Optimal Policy ◽

Queueing System ◽

Sufficient Conditions ◽

System Capacity ◽

Average Reward ◽

Finite Capacity ◽

Long Run ◽

Optimal Policies ◽

Service Rates ◽

Long Run Average Reward

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

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Bias optimal admission control policies for a multiclass nonstationary queueing system

Journal of Applied Probability ◽

10.1239/jap/1019737985 ◽

2002 ◽

Vol 39 (1) ◽

pp. 20-37 ◽

Cited By ~ 6

Author(s):

Mark E. Lewis ◽

Hayriye Ayhan ◽

Robert D. Foley

Keyword(s):

Optimal Policy ◽

Queueing System ◽

Sufficient Conditions ◽

System Capacity ◽

Average Reward ◽

Finite Capacity ◽

Long Run ◽

Optimal Policies ◽

Service Rates ◽

Long Run Average Reward

We consider a finite-capacity queueing system where arriving customers offer rewards which are paid upon acceptance into the system. The gatekeeper, whose objective is to ‘maximize’ rewards, decides if the reward offered is sufficient to accept or reject the arriving customer. Suppose the arrival rates, service rates, and system capacity are changing over time in a known manner. We show that all bias optimal (a refinement of long-run average reward optimal) policies are of threshold form. Furthermore, we give sufficient conditions for the bias optimal policy to be monotonic in time. We show, via a counterexample, that if these conditions are violated, the optimal policy may not be monotonic in time or of threshold form.

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OPTIMAL CONTROL OF A TWO-SERVER QUEUEING SYSTEM WITH FAILURES

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964814000114 ◽

2014 ◽

Vol 28 (4) ◽

pp. 489-527 ◽

Cited By ~ 18

Author(s):

Erhun Özkan ◽

Jeffrey P. Kharoufeh

Keyword(s):

Process Model ◽

Queueing System ◽

Threshold Policy ◽

Long Run ◽

Reliability Characteristics ◽

Markov Decision ◽

Service Rates ◽

Number Of Customers ◽

Random Failures ◽

Main Model

We consider the problem of controlling a two-server Markovian queueing system with heterogeneous servers. The servers are differentiated by their service rates and reliability attributes (i.e., the slower server is perfectly reliable, whereas the faster server is subject to random failures). The aim is to dynamically route customers at arrival, service completion, server failure, and server repair epochs to minimize the long-run average number of customers in the system. Using a Markov decision process model, we prove that it is always optimal to route customers to the faster server when it is available, irrespective of its failure and repair rates, if the system is stable. For the slower server, there exists an optimal threshold policy that depends on the queue length and the state of the faster server. Additionally, we analyze a variant of the main model in which there are multiple unreliable servers with identical service rates, but distinct reliability characteristics. For that case it is always optimal to route customers to idle servers, and the optimal policy is insensitive to the servers’ reliability characteristics.

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Analysis of the Optimal Resource Allocation for a Tandem Queueing System

Mathematical Problems in Engineering ◽

10.1155/2017/5964272 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Zaiming Liu ◽

Wei Deng ◽

Gang Chen

Keyword(s):

Optimal Policy ◽

Optimal Allocation ◽

Queueing System ◽

Service Rate ◽

Allocation Policy ◽

Long Run ◽

Markov Decision ◽

Upstream Station ◽

Optimal Resource ◽

Resource Cost

We study a controllable two-station tandem queueing system, where customers (jobs) must first be processed at upstream station and then the downstream station. A manager dynamically allocates the service resource to each station to adjust the service rate, leading to a tradeoff between the holding cost and resource cost. The goal of the manager is to find the optimal policy to minimize the long-run average costs. The problem is constructed as a Markov decision process (MDP). In this paper, we consider the model in which the resource cost and service rate functions are more general than linear. We derive the monotonicity of the optimal allocation policy by the quasiconvexity properties of the value function. Furthermore, we obtain the relationship between the two stations’ optimal policy and conditions under which the optimal policy is unique and has the bang-bang control property. Finally, we provide some numerical experiments to illustrate these results.

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Mathematical Model of an Industrial Distributed Ledger as a Queueing System with Multiple Tickets of Unlimited Depth

2021 International Conference on Industrial Engineering, Applications and Manufacturing (ICIEAM) ◽

10.1109/icieam51226.2021.9446446 ◽

2021 ◽

Author(s):

Vladimir Evsin ◽

Svetlana Shirobokova ◽

Sergei Vorobyev

Keyword(s):

Mathematical Model ◽

Queueing System ◽

Distributed Ledger

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A Pot-Like Vibrational Microfluidic Rotational Motor

Micromachines ◽

10.3390/mi12020177 ◽

2021 ◽

Vol 12 (2) ◽

pp. 177

Author(s):

Suzana Uran ◽

Matjaž Malok ◽

Božidar Bratina ◽

Riko Šafarič

Keyword(s):

Mathematical Model ◽

Rotational Speed ◽

Mechanical Energy ◽

Real Life ◽

Frequency Region ◽

Theoretical Research ◽

Practical Challenge ◽

The Mathematical Model ◽

Motor Structure ◽

Proper Balance

Constructing a micro-sized microfluidic motor always involves the problem of how to transfer the mechanical energy out of the motor. The paper presents several experiments with pot-like microfluidic rotational motor structures driven by two perpendicular sine and cosine vibrations with amplitudes around 10 μm in the frequency region from 200 Hz to 500 Hz. The extensive theoretical research based on the mathematical model of the liquid streaming in a pot-like structure was the base for the successful real-life laboratory application of a microfluidic rotational motor. The final microfluidic motor structure allowed transferring the rotational mechanical energy out of the motor with a central axis. The main practical challenge of the research was to find the proper balance between the torque, due to friction in the bearings and the motor’s maximal torque. The presented motor, with sizes 1 mm by 0.6 mm, reached the maximal rotational speed in both directions between −15 rad/s to +14 rad/s, with the estimated maximal torque of 0.1 pNm. The measured frequency characteristics of vibration amplitudes and phase angle between the directions of both vibrational amplitudes and rotational speed of the motor rotor against frequency of vibrations, allowed us to understand how to build the pot-like microfluidic rotational motor.

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