scholarly journals Analyzing a degenerate buffer with general inter-arrival and service times in discrete time

2007 ◽  
Vol 56 (3-4) ◽  
pp. 203-212 ◽  
Author(s):  
W. Rogiest ◽  
K. Laevens ◽  
J. Walraevens ◽  
H. Bruneel
Keyword(s):  
Discrete Time ◽  
Service Times

scholarly journals Performance analysis of a discrete-time two-class global-FCFS queue with two servers and geometric service times

2017 ◽  
Vol 109 ◽  
pp. 34-51 ◽  
Author(s):  
Herwig Bruneel ◽  
Willem Mélange ◽  
Joris Walraevens ◽  
Stijn De Vuyst ◽  
Dieter Claeys
Keyword(s):  
Performance Analysis ◽  
Discrete Time ◽  
Global Fcfs ◽  
Service Times

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.

DISCRETE-TIME GIX/GEO/1/N QUEUE WITH WORKING VACATIONS AND VACATION INTERRUPTION

2014 ◽  
Vol 31 (01) ◽  
pp. 1450003 ◽  
Author(s):  
SHAN GAO ◽  
ZAIMING LIU ◽  
QIWEN DU
Keyword(s):  
Discrete Time ◽  
Finite Buffer ◽  
Waiting Time Distribution ◽  
Service Period ◽  
Imbedded Markov Chain ◽  
Working Vacations ◽  
Vacation Interruption ◽  
Service Times ◽  
System Length ◽  
Vacation Period

In this paper, we study a discrete-time finite buffer batch arrival queue with multiple geometric working vacations and vacation interruption: the server serves the customers at the lower rate rather than completely stopping during the vacation period and can come back to the normal working level once there are customers after a service completion during the vacation period, i.e., a vacation interruption happens. The service times during a service period, service times during a vacation period and vacation times are geometrically distributed. The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques. We obtain steady-state system length distributions at pre-arrival, arbitrary and outside observer's observation epochs. We also present probability generation function (p.g.f.) of actual waiting-time distribution in the system and some performance measures.

scholarly journals Discrete-time multiserver queues with geometric service times

2004 ◽  
Vol 31 (1) ◽  
pp. 81-99 ◽  
Author(s):  
Peixia Gao ◽  
Sabine Wittevrongel ◽  
Herwig Bruneel
Keyword(s):  
Discrete Time ◽  
Multiserver Queues ◽  
Service Times

The infinite server queue with semi-Markovian arrivals and negative exponential services

1972 ◽  
Vol 9 (1) ◽  
pp. 178-184 ◽  
Author(s):  
Marcel F. Neuts ◽  
Shun-Zer Chen
Keyword(s):  
Discrete Time ◽  
Infinite Number ◽  
Queue Length ◽  
Markovian Arrival Process ◽  
Arrival Process ◽  
Infinite Server ◽  
Server Queue ◽  
Service Times ◽  
Negative Exponential ◽  
Stationary Probabilities

The queue with an infinite number of servers with a semi-Markovian arrival process and with negative exponential service times is studied. The queue length process and the type of the last customer to join the queue before time t are studied jointly, both in continuous and in discrete time. Limiting stationary probabilities are also obtained.

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