Average optimal policies in a controlled queueing system with dual admission control

2001 ◽  
Vol 38 (02) ◽  
pp. 369-385 ◽  
Author(s):  
Mark E. Lewis
Keyword(s):  
Admission Control ◽  
Manufacturing Systems ◽  
Queueing System ◽  
Service Rate ◽  
Average Reward ◽  
Long Run ◽  
Switching Curve ◽  
Multiple Tasks ◽  
Optimal Policies ◽  
Number Of Customers

We consider a controlled M/M/1 queueing system where customers may be subject to two potential rejections. The first occurs upon arrival and is dependent on the number of customers in the queue and the service rate of the customer currently in service. The second, which may or may not occur, occurs immediately prior to the customer receiving service. That is, after each service completion the customer in the front of the queue is assessed and the service rate of that customer is revealed. If the second decision-maker recommends rejection, the customer is denied service with a fixed probability. We show the existence of long-run average optimal monotone switching-curve policies. Further, we show that the average reward is increasing in the probability that the second decision-maker's recommendation of rejection is honored. Applications include call centers with delayed classifications and manufacturing systems when the server is responsible for multiple tasks.

Average optimal policies in a controlled queueing system with dual admission control

2001 ◽  
Vol 38 (2) ◽  
pp. 369-385 ◽  
Author(s):  
Mark E. Lewis
Keyword(s):  
Admission Control ◽  
Manufacturing Systems ◽  
Queueing System ◽  
Service Rate ◽  
Average Reward ◽  
Long Run ◽  
Switching Curve ◽  
Multiple Tasks ◽  
Optimal Policies ◽  
Number Of Customers

We consider a controlled M/M/1 queueing system where customers may be subject to two potential rejections. The first occurs upon arrival and is dependent on the number of customers in the queue and the service rate of the customer currently in service. The second, which may or may not occur, occurs immediately prior to the customer receiving service. That is, after each service completion the customer in the front of the queue is assessed and the service rate of that customer is revealed. If the second decision-maker recommends rejection, the customer is denied service with a fixed probability. We show the existence of long-run average optimal monotone switching-curve policies. Further, we show that the average reward is increasing in the probability that the second decision-maker's recommendation of rejection is honored. Applications include call centers with delayed classifications and manufacturing systems when the server is responsible for multiple tasks.

BIAS OPTIMALITY IN A QUEUE WITH ADMISSION CONTROL

1999 ◽  
Vol 13 (3) ◽  
pp. 309-327 ◽  
Author(s):  
Mark E. Lewis ◽  
Hayriye Ayhan ◽  
Robert D. Foley
Keyword(s):  
Admission Control ◽  
Queueing System ◽  
Average Reward ◽  
Objective Functions ◽  
Finite Capacity ◽  
Long Run ◽  
Blackwell Optimality ◽  
Optimal Policies ◽  
Bias Optimality ◽  
Long Run Average Reward

We consider a finite capacity queueing system in which each arriving customer offers a reward. A gatekeeper decides based on the reward offered and the space remaining whether each arriving customer should be accepted or rejected. The gatekeeper only receives the offered reward if the customer is accepted. A traditional objective function is to maximize the gain, that is, the long-run average reward. It is quite possible, however, to have several different gain optimal policies that behave quite differently. Bias and Blackwell optimality are more refined objective functions that can distinguish among multiple stationary, deterministic gain optimal policies. This paper focuses on describing the structure of stationary, deterministic, optimal policies and extending this optimality to distinguish between multiple gain optimal policies. We show that these policies are of trunk reservation form and must occur consecutively. We then prove that we can distinguish among these gain optimal policies using the bias or transient reward and extend to Blackwell optimality.

Bias optimal admission control policies for a multiclass nonstationary queueing system

2002 ◽  
Vol 39 (01) ◽  
pp. 20-37 ◽  
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.

TWO-CLASS ROUTING WITH ADMISSION CONTROL AND STRICT PRIORITIES

2017 ◽  
Vol 32 (2) ◽  
pp. 163-178 ◽  
Author(s):  
Kenneth C. Chong ◽  
Shane G. Henderson ◽  
Mark E. Lewis
Keyword(s):  
Admission Control ◽  
Numerical Study ◽  
Reward Structure ◽  
Long Run ◽  
Switching Curve ◽  
Optimal Policies ◽  
Markov Decision ◽  
Average Reward Criteria ◽  
The Value Function ◽  
Long Run Average Reward

We consider the problem of routing and admission control in a loss system featuring two classes of arriving jobs (high-priority and low-priority jobs) and two types of servers, in which decision-making for high-priority jobs is forced, and rewards influence the desirability of each of the four possible routing decisions. We seek a policy that maximizes expected long-run reward, under both the discounted reward and long-run average reward criteria, and formulate the problem as a Markov decision process. When the reward structure favors high-priority jobs, we demonstrate that there exists an optimal monotone switching curve policy with slope of at least −1. When the reward structure favors low-priority jobs, we demonstrate that the value function, in general, lacks structure, which complicates the search for structure in optimal policies. However, we identify conditions under which optimal policies can be characterized in greater detail. We also examine the performance of heuristic policies in a brief numerical study.

Bias optimal admission control policies for a multiclass nonstationary queueing system

2002 ◽  
Vol 39 (1) ◽  
pp. 20-37 ◽  
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.

Dynamic pricing in a two-class queueing system with arrival and service rate control

2020 ◽  
Author(s):  
Shuangfeng Ma ◽  
Wei Guo
Keyword(s):  
Rate Control ◽  
Dynamic Pricing ◽  
Queueing System ◽  
Recursive Algorithm ◽  
Optimization Theory ◽  
Service Rate ◽  
Long Run ◽  
Holding Cost ◽  
Service Rates ◽  
Number Of Customers

Abstract Dynamic pricing in a two-class queueing system with adjustable arrival and service rates is considered in this paper. We initially take the adjustable rates into account to maximize the long-run average social welfare and further establish matched dynamic prices to lead two distinct types of customers’ behavior. For the rate-setting problems, we apply the sensitivity-based optimization theory and an iterative algorithm to investigate the two types of customers’ optimal arrival and service rates. Next, we apply the results obtained from rate-setting problems to acquire the expected delay time by recursive algorithm and demonstrate the optimal prices formulas for multiple customers explicitly. Finally, we carry out some numerical experiments to illustrate our consequence and the performance between two kinds of customers with different level of holding cost. It appears that under low holding cost, the optimal prices for two kinds of customers are monotonically increasing in the number of customers regardless of classes, but under high holding cost, the optimal prices for the customers who have low waiting cost may drop when the number of the other class rises.

Optimal Thresholds of an Infinite Buffer Discrete-Time Two-Server System with Triadic Policy

2011 ◽  
Vol 2 (4) ◽  
pp. 75-88
Author(s):  
Veena Goswami ◽  
G. B. Mund
Keyword(s):  
Discrete Time ◽  
Queueing System ◽  
Minimum Cost ◽  
Service Rate ◽  
Closed Form Solutions ◽  
Optimal Thresholds ◽  
Optimal Service ◽  
Number Of Customers ◽  
System Operating ◽  
Server System

This paper analyzes a discrete-time infinite-buffer Geo/Geo/2 queue, in which the number of servers can be adjusted depending on the number of customers in the system one at a time at arrival or at service completion epoch. Analytical closed-form solutions of the infinite-buffer Geo/Geo/2 queueing system operating under the triadic (0, Q N, M) policy are derived. The total expected cost function is developed to obtain the optimal operating (0, Q N, M) policy and the optimal service rate at minimum cost using direct search method. Some performance measures and sensitivity analysis have been presented.

Optimality of Randomized Trunk Reservation

1994 ◽  
Vol 8 (4) ◽  
pp. 463-489 ◽  
Author(s):  
Eugene A. Feinberg ◽  
Martin I. Reiman
Keyword(s):  
Optimal Policy ◽  
Queueing System ◽  
Blocking Probability ◽  
Average Reward ◽  
Constrained Problem ◽  
Optimal Policies ◽  
Customer Type ◽  
Time Subject

We consider a controlled queueing system that is a generalization of the M/M/c/W queue. There are m types of customers that arrive according to independent Poisson processes. Service times are exponential and independent and do not depend on the customer type. There is room in the system for a total of N customers; if there are N customers in the system, new arrivals are lost. Type j customers are more profitable than type (j + 1 ) customers, j = 2,…, m —, and type 1 customers are at least as profitable as type 2 customers. The allowed control is to accept or reject customers at arrival. No preemption of customers in service is allowed. The goal is to maximize the average reward per unit of time subject to a constraint that the blocking probability of type 1 customers is no greater than a given level.For an M/M/c/c system without a constraint, Miller [12] proved that an optimal policy has a simple threshold structure. We show that, for the constrained problem described above, an optimal policy has a similar structure, but one of the thresholds might have to be randomized. We also derive an algorithm that constructs an optimal policy and describe other forms of optimal policies.

ANALYSIS OF A BULK QUEUE WITH FAST AND SLOW SERVICE RATES AND MULTIPLE VACATIONS

2005 ◽  
Vol 22 (02) ◽  
pp. 239-260 ◽  
Author(s):  
R. ARUMUGANATHAN ◽  
K. S. RAMASWAMI
Keyword(s):  
Performance Measures ◽  
Queue Length ◽  
Queueing System ◽  
Cost Model ◽  
Probability Generating Function ◽  
Service Rate ◽  
Multiple Vacations ◽  
Bulk Queue ◽  
Service Rates ◽  
Number Of Customers

We analyze a Mx/G(a,b)/1 queueing system with fast and slow service rates and multiple vacations. The server does the service with a faster rate or a slower rate based on the queue length. At a service completion epoch (or) at a vacation completion epoch if the number of customers waiting in the queue is greater than or equal to N (N > b), then the service is rendered at a faster rate, otherwise with a slower service rate. After finishing a service, if the queue length is less than 'a' the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than 'a' he leaves for another vacation and so on until he finally finds atleast 'a' customers waiting for service. After a service (or) a vacation, if the server finds atleast 'a' customers waiting for service say ξ, then he serves a batch of min (ξ, b) customers, where b ≥ a. We derive the probability generating function of the queue size at an arbitrary time. Various performance measures are obtained. A cost model is discussed with a numerical solution.

scholarly journals Finite M/M/1 retrial model with changeable service rate

2021 ◽  
Vol 56 (1) ◽  
pp. 96-102
Author(s):  
M.S. Bratiichuk ◽  
A.A. Chechelnitsky ◽  
I.Ya. Usar
Keyword(s):  
Queueing System ◽  
Service Rate ◽  
Numerical Examples ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
Explicit Formulae ◽  
Number Of Customers ◽  
Theoretical Results

The article deals with M/M/1 -type retrial queueing system with finite orbit. It is supposedthat service rate depends on the loading of the system. The explicit formulae for ergodicdistribution of the number of customers in the system are obtained. The theoretical results areillustrated by numerical examples.

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