On the joint distribution of an infinite-buffer discrete-time batch-size-dependent service queue with single and multiple vacations

2021 ◽  
pp. 1-36
Author(s):  
Nilanjan Nandy ◽  
Sourav Pradhan
Keyword(s):  
Discrete Time ◽  
Joint Distribution ◽  
Batch Size ◽  
Multiple Vacations ◽  
Size Dependent

scholarly journals Queue Length and Server Content Distribution in an Infinite-Buffer Batch-Service Queue with Batch-Size-Dependent Service

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
U. C. Gupta ◽  
S. Pradhan
Keyword(s):  
Joint Distribution ◽  
Probability Generating Function ◽  
Batch Size ◽  
Batch Service ◽  
Supplementary Variable ◽  
Variable Technique ◽  
Size Dependent ◽  
Poisson Arrival ◽  
Bivariate Probability ◽  
Server Content

We analyze an infinite-buffer batch-size-dependent batch-service queue with Poisson arrival and arbitrarily distributed service time. Using supplementary variable technique, we derive a bivariate probability generating function from which the joint distribution of queue and server content at departure epoch of a batch is extracted and presented in terms of roots of the characteristic equation. We also obtain the joint distribution of queue and server content at arbitrary epoch. Finally, the utility of analytical results is demonstrated by the inclusion of some numerical examples which also includes the investigation of multiple zeros.

Some ARMA models for dependent sequences of poisson counts

1988 ◽  
Vol 20 (4) ◽  
pp. 822-835 ◽  
Author(s):  
Ed Mckenzie
Keyword(s):  
Asymptotic Behaviour ◽  
Discrete Time ◽  
Joint Distribution ◽  
Autoregressive Process ◽  
Two Dimensional ◽  
Arma Models ◽  
Time Reversibility ◽  
Vector Autoregressive ◽  
Arma Processes ◽  
Vector Autoregressive Process

A family of models for discrete-time processes with Poisson marginal distributions is developed and investigated. They have the same correlation structure as the linear ARMA processes. The joint distribution of n consecutive observations in such a process is derived and its properties discussed. In particular, time-reversibility and asymptotic behaviour are considered in detail. A vector autoregressive process is constructed and the behaviour of its components, which are Poisson ARMA processes, is considered. In particular, the two-dimensional case is discussed in detail.

scholarly journals Selecting batch size in discrete-time two-phase queuing system

2008 ◽  
Vol 47 (11-12) ◽  
pp. 1246-1253 ◽  
Author(s):  
Subrata Saha ◽  
Attahiru Sule Alfa
Keyword(s):  
Discrete Time ◽  
Queuing System ◽  
Batch Size ◽  
Two Phase

Asymptotic behavior of near-critical multitype branching processes

1991 ◽  
Vol 28 (03) ◽  
pp. 512-519 ◽  
Author(s):  
Fima C. Klebaner
Keyword(s):  
Asymptotic Behavior ◽  
Population Size ◽  
Discrete Time ◽  
Growth Rates ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Limiting Distribution ◽  
Size Dependent ◽  
Generalized Gamma ◽  
Multitype Branching Processes

Sufficient conditions for survival and extinction of multitype population-size-dependent branching processes in discrete time are obtained. Growth rates are determined on the set of divergence to infinity. The limiting distribution of a properly normalized process can be generalized gamma, normal or degenerate.

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