Markovian Queueing System for Bulk Arrival and Retrial Attempts with Multiple Vacation Policy

2021 ◽  
Vol 67 (1) ◽  
pp. 21-28
Author(s):  
Sadhna Singh ◽  
Srivastava R K
Keyword(s):  
Queueing System ◽  
Multiple Vacation ◽  
Bulk Arrival

scholarly journals On a bulk queueing system with impatient customers

1998 ◽  
Vol 3 (6) ◽  
pp. 539-554 ◽  
Author(s):  
Lotfi Tadj ◽  
Lakdere Benkherouf ◽  
Lakhdar Aggoun
Keyword(s):  
Steady State ◽  
Queue Length ◽  
Queueing System ◽  
Impatient Customers ◽  
Ergodicity Condition ◽  
Bulk Service ◽  
Bulk Arrival ◽  
Steady State Probabilities ◽  
System Characteristics

We consider a bulk arrival, bulk service queueing system. Customers are served in batches ofrunits if the queue length is not less thanr. Otherwise, the server delays the service until the number of units in the queue reaches or exceeds levelr. We assume that unserved customers may get impatient and leave the system. An ergodicity condition and steady-state probabilities are derived. Various system characteristics are also computed.

scholarly journals A bulk queueing system under N-policy with bilevel service delay discipline and start-up time

1993 ◽  
Vol 6 (4) ◽  
pp. 359-384 ◽  
Author(s):  
David C. R. Muh
Keyword(s):  
Queue Length ◽  
Queueing System ◽  
Probability Generating Function ◽  
Single Server ◽  
Numerical Examples ◽  
Queueing Process ◽  
Poisson Input ◽  
Service Delay ◽  
Start Up ◽  
Bulk Arrival

The author studies the queueing process in a single-server, bulk arrival and batch service queueing system with a compound Poisson input, bilevel service delay discipline, start-up time, and a fixed accumulation level with control operating policy. It is assumed that when the queue length falls below a predefined level r(≥1), the system, with server capacity R, immediately stops service until the queue length reaches or exceeds the second predefined accumulation level N(≥r). Two cases, with N≤R and N≥R, are studied.The author finds explicitly the probability generating function of the stationary distribution of the queueing process and gives numerical examples.

scholarly journals Mathematical Models of Mb/M/1 Bulk Arrival Queueing System

2014 ◽  
Vol 10 (1) ◽  
pp. 184-191 ◽  
Author(s):  
Sushil Ghimire ◽  
R. P. Ghimire ◽  
Gyan Bahadur Thapa
Keyword(s):  
Mathematical Model ◽  
Function Method ◽  
Queueing System ◽  
Batch Size ◽  
Queueing Model ◽  
Mean Waiting Time ◽  
Bulk Arrival ◽  
Number Of Customers ◽  
The Mathematical Model ◽  
Mean Time

 This paper deals with the study of bulk queueing model with the fixed batch size ‘b’ and customers arrive to the system with Poisson fashion with the rate λ and are severed exponentially with the rate μ. On formulating the mathematical model, we obtain the expressions for mean waiting time in the queue, mean time spent in the system, mean number of customers/work pieces in the queue and in the system by using generating function method. Some numerical illustrations are also obtained by using MATLAB-7 so as to show the applicability of the model under study.DOI: http://dx.doi.org/10.3126/jie.v10i1.10899Journal of the Institute of Engineering, Vol. 10, No. 1, 2014, pp. 184–191

scholarly journals Discrete-Time Bulk Queueing System with Variable Service Capacity Depending on Previous Service Time

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Yutae Lee
Keyword(s):  
Generating Function ◽  
Discrete Time ◽  
Service Time ◽  
Queue Length ◽  
Queueing System ◽  
Function Technique ◽  
Supplementary Variable ◽  
Service Capacity ◽  
Bulk Service ◽  
Bulk Arrival

This paper considers a discrete-time bulk-arrival bulk-service queueing system with variable service capacity, where the service capacity varies depending on the previous service time. Using the supplementary variable method and the generating function technique, we obtain the queue length distributions at arbitrary slot boundaries and service completion epochs.

scholarly journals Identification of waiting time distribution ofM/G/1,Mx/G/1,GIr/M/1queueing systems

1988 ◽  
Vol 11 (3) ◽  
pp. 589-597
Author(s):  
A. Ghosal ◽  
S. Madan
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing System ◽  
Numerical Study ◽  
Queueing Models ◽  
Single Server ◽  
Waiting Time Distribution ◽  
System A ◽  
Bulk Arrival

This paper brings out relations among the moments of various orders of the waiting time of the1st customer and a randomly selected customer of an arrival group for bulk arrivals queueing models, and as well as moments of the waiting time (in queue) forM/G/1queueing system. A numerical study of these relations has been developed in order to find the(β1,β2)measures of waiting time distribution in a comutable form. On the basis of these measures one can look into the nature of waiting time distribution of bulk arrival queues and the single serverM/G/1queue.

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