Vacation policies in an M/G/1 type queueing system with finite capacity

1988 ◽  
Vol 3 (1) ◽  
pp. 41-52 ◽  
Author(s):  
Jacqueline Loris-Teghem
Keyword(s):  
Queueing System ◽  
Finite Capacity

scholarly journals PERFORMANCE MEASURES FOR THE TWO-NODE QUEUE WITH FINITE BUFFERS

2019 ◽  
Vol 34 (4) ◽  
pp. 522-549
Author(s):  
Yanting Chen ◽  
Xinwei Bai ◽  
Richard J. Boucherie ◽  
Jasper Goseling
Keyword(s):  
Random Walk ◽  
Performance Measures ◽  
Approximation Scheme ◽  
Queueing System ◽  
Original Model ◽  
Finite Capacity ◽  
Tandem Queue ◽  
Finite Buffers ◽  
Perturbed Random Walk ◽  
Markov Reward

We consider a two-node queue modeled as a two-dimensional random walk. In particular, we consider the case that one or both queues have finite buffers. We develop an approximation scheme based on the Markov reward approach to error bounds in order to bound performance measures of such random walks. The approximation scheme is developed in terms of a perturbed random walk in which the transitions along the boundaries are different from those in the original model and the invariant measure of the perturbed random walk is of product-form. We then apply this approximation scheme to a tandem queue and some variants of this model, for the case that both buffers are finite. The modified approximation scheme and the corresponding applications for a two-node queueing system in which only one of the buffers has finite capacity have also been discussed.

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.

The GI/G/1 queue with uniformly limited virtual waiting times; the finite dam

1980 ◽  
Vol 12 (2) ◽  
pp. 501-516 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Water Supply ◽  
Analytical Method ◽  
Busy Period ◽  
Queueing System ◽  
Waiting Times ◽  
Fixed Interval ◽  
Finite Capacity ◽  
Queueing Process ◽  
Finite Dam

This paper studies the GI/G/1 queueing system in which no customer can stay longer than a fixed interval D. This is also a model for the dam with finite capacity, instantaneous water supply and constant release rule. Using analytical method together with the property that the queueing process ‘starts anew’ probabilistically whenever an arriving customer initiates a busy period, we obtain various transient and stationary results for the system.

A solvable model for a finite-capacity queueing system

1985 ◽  
Vol 22 (4) ◽  
pp. 903-911 ◽  
Author(s):  
V. Giorno ◽  
C. Negri ◽  
A. G. Nobile
Keyword(s):  
Queueing System ◽  
Waiting Times ◽  
Queueing Systems ◽  
Solvable Model ◽  
Probability Density Functions ◽  
Single Server ◽  
Finite Capacity ◽  
System Service ◽  
Transient Probabilities ◽  
Number Of Customers

Single–server–single-queue–FIFO-discipline queueing systems are considered in which at most a finite number of customers N can be present in the system. Service and arrival rates are taken to be dependent upon that state of the system. Interarrival intervals, service intervals, waiting times and busy periods are studied, and the results obtained are used to investigate the features of a special queueing model characterized by parameters (λ (Ν –n), μn). This model retains the qualitative features of the C-model proposed by Conolly [2] and Chan and Conolly [1]. However, quite unlike the latter, it also leads to closed-form expressions for the transient probabilities, the interarrival and service probability density functions and their moments, as well as the effective interarrival and service densities and their moments. Finally, some computational results are given to compare the model discussed in this paper with the C-model.

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.

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