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.

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.

scholarly journals Estimating the Probability of Ruin for Variable Premiums by Simulation

1996 ◽  
Vol 26 (1) ◽  
pp. 93-105 ◽  
Author(s):  
Frédéric Michaud
Keyword(s):  
Sample Path ◽  
Risk Theory ◽  
Single Server ◽  
Single Server Queue ◽  
Storage Process ◽  
Probability Of Ruin ◽  
Surplus Process ◽  
Special Cases ◽  
Server Queue ◽  
Waiting Time Process

AbstractThere is a duality between the surplus process of classical risk theory and the single-server queue. It follows that the probability of ruin can be retrieved from a single sample path of the waiting time process of the single-server queue. In this paper, premiums are allowed to vary. It has been shown that the stationary distribution of a corresponding storage process is equal to the survival probability (with variable premiums). Thus by simulation of the corresponding storage process, the probability of ruin can be obtained. The special cases where the surplus earns interest and the premiums are charged by layers are considered and illustrated numerically.

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.

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).

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).

Simulation and Queueing Theory Applied to a Single-server Queue with Advertising and Balking

1993 ◽  
Vol 44 (4) ◽  
pp. 407-414 ◽  
Author(s):  
A van Ackere ◽  
P Ninios
Keyword(s):  
Queueing Theory ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

Corrigendum to “The distribution of the number of arrivals in a subinterval of a busy period of a single server queue”

2008 ◽  
Vol 59 (2) ◽  
pp. 87-93 ◽  
Author(s):  
A. Novak ◽  
P. Taylor ◽  
D. Veitch
Keyword(s):  
Busy Period ◽  
Single Server ◽  
Single Server Queue ◽  
Server Queue

A Light Traffic Approximation for a Single-Server Queue

1984 ◽  
Vol 9 (4) ◽  
pp. 624-628 ◽  
Author(s):  
D. J. Daley ◽  
T. Rolski
Keyword(s):  
Single Server ◽  
Single Server Queue ◽  
Light Traffic ◽  
Server Queue
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