Delay in a Discrete-Time Queueing Model with Batch Arrivals and Batch Services

2008 ◽  
Author(s):  
Dieter Claeys ◽  
Koenraad Laevens ◽  
Joris Walraevens ◽  
Herwig Bruneel
Keyword(s):  
Discrete Time ◽  
Queueing Model ◽  
Batch Arrivals ◽  
Batch Services

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

Analysis of a discrete-time GI–G–1 queueing model subjected to bursty interruptions

2003 ◽  
Vol 30 (1) ◽  
pp. 139-153 ◽  
Author(s):  
Dieter Fiems ◽  
Bart Steyaert ◽  
Herwig Bruneel
Keyword(s):  
Discrete Time ◽  
Queueing Model

Queueing networks with instantaneous movements: a unified approach by quasi-reversibility

2000 ◽  
Vol 32 (01) ◽  
pp. 284-313 ◽  
Author(s):  
Xiuli Chao ◽  
Masakiyo Miyazawa
Keyword(s):  
Queueing Networks ◽  
Product Form ◽  
Unified Approach ◽  
Stationary Distributions ◽  
Batch Arrivals ◽  
Unified View ◽  
Batch Services ◽  
Product Form Queueing Networks

In this paper we extend the notion of quasi-reversibility and apply it to the study of queueing networks with instantaneous movements and signals. The signals treated here are considerably more general than those in the existing literature. The approach not only provides a unified view for queueing networks with tractable stationary distributions, it also enables us to find several new classes of product form queueing networks, including networks with positive and negative signals that instantly add or remove customers from a sequence of nodes, networks with batch arrivals, batch services and assembly-transfer features, and models with concurrent batch additions and batch deletions along a fixed or a random route of the network.

The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution

1978 ◽  
Vol 15 (3) ◽  
pp. 590-601 ◽  
Author(s):  
Do Le Minh
Keyword(s):  
Discrete Time ◽  
Service Time ◽  
Time Distribution ◽  
Single Server ◽  
Service Time Distribution ◽  
Queueing Model ◽  
Compound Poisson ◽  
Poisson Input ◽  
Server Queue ◽  
General Service

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution.All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.

scholarly journals Discrete- Time Queueing Model Geox/G/ꚙ with Bulk Arrival Rule

2020 ◽  
Vol 9 (3) ◽  
pp. 2585-2589
Keyword(s):  
Discrete Time ◽  
Geometric Distribution ◽  
Transient State ◽  
State Solution ◽  
General Distribution ◽  
Queueing Model ◽  
Service Times ◽  
Bulk Arrival ◽  
Number Of Customers

A discrete time queueing model is considered to estimate of the number of customers in the system. The arrivals, which are in groups of size X, inter-arrivals times and service times are distributed independent. The inter-arrivals fallows geometric distribution with parameter p and service times follows general distribution with parameter µ, we have derive the various transient state solution along with their moments and numerical illustrations in this paper.

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