The single-server queue with random service output

1975 ◽  
Vol 12 (04) ◽  
pp. 763-778 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Service Process ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
Single Server Queue ◽  
Independent Increments ◽  
Server Queue ◽  
Work Done

In this paper a problem arising in queueing and dam theory is studied. We shall consider a G/G*/1 queueing model, i.e., a G/G/1 queueing model of which the service process is a separable centered process with stationary independent increments. This is a generalisation of the well-known G/G/1 model with constant service rate. Several results concerning the amount of work done by the server, the busy cycles etc., are derived, mainly using the well-known method of Pollaczek. Emphasis is laid on the similarities and dissimilarities between the results of the ‘classical’ G/G/1 model and the G/G*/1 model.

The single-server queue with random service output

1975 ◽  
Vol 12 (4) ◽  
pp. 763-778 ◽  
Author(s):  
O. J. Boxma
Keyword(s):  
Service Process ◽  
Service Rate ◽  
Single Server ◽  
Queueing Model ◽  
Single Server Queue ◽  
Independent Increments ◽  
Server Queue ◽  
Work Done

In this paper a problem arising in queueing and dam theory is studied. We shall consider a G/G*/1 queueing model, i.e., a G/G/1 queueing model of which the service process is a separable centered process with stationary independent increments. This is a generalisation of the well-known G/G/1 model with constant service rate.Several results concerning the amount of work done by the server, the busy cycles etc., are derived, mainly using the well-known method of Pollaczek. Emphasis is laid on the similarities and dissimilarities between the results of the ‘classical’ G/G/1 model and the G/G*/1 model.

BROWNIAN MOTION MINUS THE INDEPENDENT INCREMENTS: REPRESENTATION AND QUEUING APPLICATION

2020 ◽  
pp. 1-25
Author(s):  
Kerry Fendick
Keyword(s):  
Brownian Motion ◽  
Maximum Likelihood ◽  
Markov Process ◽  
Maximum Likelihood Estimators ◽  
Single Server ◽  
Single Server Queue ◽  
Stationary Increments ◽  
Transient Distribution ◽  
Independent Increments ◽  
Server Queue

This paper relaxes assumptions defining multivariate Brownian motion (BM) to construct processes with dependent increments as tractable models for problems in engineering and management science. We show that any Gaussian Markov process starting at zero and possessing stationary increments and a symmetric smooth kernel has a parametric kernel of a particular form, and we derive the unique unbiased, jointly sufficient, maximum-likelihood estimators of those parameters. As an application, we model a single-server queue driven by such a process and derive its transient distribution conditional on its history.

Constrained Average Cost Markov Decision Chains

1993 ◽  
Vol 7 (1) ◽  
pp. 69-83 ◽  
Author(s):  
Linn I. Sennott
Keyword(s):  
Rate Control ◽  
Operating Cost ◽  
Service Rate ◽  
Single Server ◽  
Single Server Queue ◽  
Stationary Policy ◽  
Server Queue ◽  
Markov Decision ◽  
Average Operating ◽  
Holding Cost

A Markov decision chain with denumerable state space incurs two types of costs — for example, an operating cost and a holding cost. The objective is to minimize the expected average operating cost, subject to a constraint on the expected average holding cost. We prove the existence of an optimal constrained randomized stationary policy, for which the two stationary policies differ on at most one state. The examples treated are a packet communication system with reject option and a single-server queue with service rate control.

Single-Server Queue System of Shuttle Bus Performance: Federal University of Technology Akure as Case Study

2019 ◽  
Vol 5 (3) ◽  
pp. 9-14
Author(s):  
Sidiq Okwudili Ben
Keyword(s):  
Laplace Transform ◽  
Poisson Process ◽  
Service Rate ◽  
Single Server ◽  
Single Server Queue ◽  
Queue System ◽  
University Of Technology ◽  
Server Queue

This study has examined the performance of University transport bus shuttle based on utilization using a Single-server queue system which occur if arrival and service rate is Poisson distributed (single queue) (M/M/1) queue. In the methodology, Single-server queue system was modelled based on Poisson Process with the introduction of Laplace Transform. It is concluded that the performance of University transport bus shuttle is 96.6 percent which indicates a very good performance such that the supply of shuttle bus in FUTA is capable of meeting the demand.

A single server queue in discrete time with customers served in random order

1972 ◽  
Vol 9 (04) ◽  
pp. 862-867
Author(s):  
D. W. Balmer
Keyword(s):  
Discrete Time ◽  
Random Order ◽  
Single Server ◽  
Queueing Model ◽  
Traffic Intensity ◽  
Single Server Queue ◽  
Server Queue

This paper aims at showing that for the discrete time analogue of the M/G/l queueing model with service in random order and with a traffic intensity ρ > 0, the condition ρ < ∞ is sufficient in order that every customer joining the queue be served eventually, with probability one (Theorem 2).

scholarly journals Sample-Path Analysis of Single-Server Queue with Multiple Vacations

2011 ◽  
Vol 2011 ◽  
pp. 1-12 ◽  
Author(s):  
Muhammad El-Taha
Keyword(s):  
Stochastic Process ◽  
Conservation Law ◽  
Sample Path ◽  
Single Server ◽  
Queueing Model ◽  
Single Server Queue ◽  
Sample Path Analysis ◽  
Multiple Vacation ◽  
Server Queue ◽  
Background Material

We a give deterministic (sample path) proof of a result that extends the Pollaczek-Khintchine formula for a multiple vacation single-server queueing model. We also give a conservation law for the same system with multiple classes. Our results are completely rigorous and hold under weaker assumptions than those given in the literature. We do not make stochastic assumptions, so the results hold almost surely on every sample path of the stochastic process that describes the system evolution. The article is self contained in that it gives a brief review of necessary background material.

A single server queue in discrete time with customers served in random order

1972 ◽  
Vol 9 (4) ◽  
pp. 862-867 ◽  
Author(s):  
D. W. Balmer
Keyword(s):  
Discrete Time ◽  
Random Order ◽  
Single Server ◽  
Queueing Model ◽  
Traffic Intensity ◽  
Single Server Queue ◽  
Server Queue

This paper aims at showing that for the discrete time analogue of the M/G/l queueing model with service in random order and with a traffic intensity ρ > 0, the condition ρ < ∞ is sufficient in order that every customer joining the queue be served eventually, with probability one (Theorem 2).

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