General-Input Single Server Vacation Models

2006 ◽  
pp. 129-192
Author(s):  
Naishuo Tian ◽  
Zhe George Zhang
Keyword(s):  
Single Server ◽  
Server Vacation ◽  
Vacation Models

scholarly journals Entropy maximization and the busy period of some single-server vacation models

2004 ◽  
Vol 38 (3) ◽  
pp. 195-213 ◽  
Author(s):  
Jesus R. Artalejo ◽  
Maria J. Lopez-Herrero
Keyword(s):  
Busy Period ◽  
Single Server ◽  
Server Vacation ◽  
Entropy Maximization ◽  
Vacation Models

scholarly journals The BMAP/G/1 vacation queue with queue-length dependent vacation schedule

1998 ◽  
Vol 40 (2) ◽  
pp. 207-221 ◽  
Author(s):  
Yang Woo Shin ◽  
Chareles E. M. Pearce
Keyword(s):  
Queue Length ◽  
Length Distribution ◽  
Arrival Process ◽  
Service Discipline ◽  
Single Server ◽  
Server Vacation ◽  
Batch Markovian Arrival Process ◽  
Queue Length Distribution ◽  
Special Cases ◽  
Number Of Customers

AbstractWe treat a single-server vacation queue with queue-length dependent vacation schedules. This subsumes the single-server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch-Markovian arrival process (BMAP). We derive the queue-length distribution at departure epochs. By using a semi-Markov process technique, we obtain the Laplace-Stieltjes transform of the transient queue-length distribution at an arbitrary time point and its limiting distribution

scholarly journals Maximum Entropy Approach for Un-Reliable Server Vacation Queueing Model with Optional Bulk Service

2012 ◽  
Vol 23 (1) ◽  
pp. 89-113
Author(s):  
Madhu Jain, Madhu Jain,
Keyword(s):  
Maximum Entropy ◽  
Performance Measures ◽  
Probability Generating Function ◽  
Single Server ◽  
Queueing Model ◽  
Time Service ◽  
Server Vacation ◽  
Single Vacation ◽  
Bulk Service ◽  
Essential Service

In this study, we consider a single server vacation queueing model with optional bulk service and an un-reliable server. A single server provides first essential service (FES) to all arriving customers one by one; apart from essential service, he can also facilitate the additional phase of optional service (OS) in batches of fixed size b( ≥ 1), in case when the customers request for it. The server may take a single vacation whenever he finds no customers waiting in the queue to be served. Moreover, the server is subjected to unpredictable breakdown while providing the first essential service. The vacation time, service time and repair time of the server are exponentially distributed. The steady state results are obtained in terms of probability generating function for queue size distributions. By using the maximum entropy analysis (MEA), we derive various system performance measures. A comparative study is performed between the exact and approximate waiting time of the system. By taking the numerical illustrations, the sensitivity analysis is done to explore the effect of different descriptors on various performance measures.

scholarly journals ON A GENERIC CLASS OF LÉVY-DRIVEN VACATION MODELS

2009 ◽  
Vol 24 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Onno Boxma ◽  
Offer Kella ◽  
Michel Mandjes
Keyword(s):  
Steady State ◽  
Content Distribution ◽  
Levy Process ◽  
Active Period ◽  
Queuing Systems ◽  
Stieltjes Transform ◽  
Server Vacation ◽  
Vacation Models ◽  
Buffer Content ◽  
Generic Class

This article analyzes a generic class of queuing systems with server vacation. The special feature of the models considered is that the duration of the vacations explicitly depends on the buffer content evolution during the previous active period (i.e., the time elapsed since the previous vacation). During both active periods and vacations, the buffer content evolves as a Lévy process. For two specific classes of models, the Laplace–Stieltjes transform of the buffer content distribution at switching epochs between successive vacations and active periods, and in steady state, is derived.

The departure process of the M/G/1 queueing model with server vacation and exhaustive service discipline

1994 ◽  
Vol 31 (4) ◽  
pp. 1070-1082 ◽  
Author(s):  
Yinghui Tang
Keyword(s):  
Renewal Theory ◽  
Service Discipline ◽  
Time Interval ◽  
Single Server ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Departure Process ◽  
Server Vacation ◽  
Server Queue ◽  
Interdeparture Time

In this paper we study the departure process of M/G/1 queueing models with a single server vacation and multiple server vacations. The arguments employed are direct probability decomposition, renewal theory and the Laplace–Stieltjes transform. We discuss the distribution of the interdeparture time and the expected number of departures occurring in the time interval (0, t] from the beginning of the state i (i = 0, 1, 2, ···), and provide a new method for analysis of the departure process of the single-server queue.

State Dependence inM/G/1 Server-Vacation Models

1988 ◽  
Vol 36 (4) ◽  
pp. 560-565 ◽  
Author(s):  
Carl M. Harris ◽  
William G. Marchal
Keyword(s):  
State Dependence ◽  
Server Vacation ◽  
Vacation Models

scholarly journals The single server vacation queue with geometric abandonments and Bernoulli’s feedbacks

2018 ◽  
Vol 7 (2.21) ◽  
pp. 172
Author(s):  
V Vijayalakshmi ◽  
K Kalidass
Keyword(s):  
Performance Measures ◽  
Numerical Experiments ◽  
The State ◽  
Single Server ◽  
Server Vacation

In this article the behaviour of a single server vacation queue with geometric abandonments and Bernoulli’s feedbacks is carried out and various important performance measures are derived. Some numerical experiments are presented to study how the parameters of the model influence the state of the system. 

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