Queue length and waiting time analysis of a batch arrival queue with bilevel control

Lee, H. W.; Park, J. G.; Kim, B. K.; Yoon, Seung Hyun; Ahn, Boo Yong; Park, N. I.

doi:10.1016/s0305-0548(97)00057-9

Cited by 13 publications

(4 citation statements)

References 3 publications

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“…Lee and Lee (1991) examined an M/G/1 batch arrival queue with different server vacations. Batch arrival queues have been thoroughly investigated by Lee et al (1995), Yue and Cao (1997), Lee et al (1998), Bacot and Dshalalow (2001) and others. Chaudhary and Paul (2004) implemented an Npolicy to a batch arrival queue with additional service channel.…”

Section: Introductionmentioning

confidence: 99%

Optimal N-Policy for Bernoulli feedback Mx/G/1 Machining System

Varshney¹,

Singh²

2019

IJRAT

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This study applies N-policy to an M X /G/1 repairable machining system with Bernoulli feedback and general setup time. The arrival rate of the failed units depends on the state of the system which may be in buildup, setup and busy states. Supplementary variable technique is employed to obtain the probability generating function for the system queue size distribution and the mean number of failed units in the system under steady state conditions. The Laplace-Stieltjes transform of the waiting time is obtained which is further used to evaluate its mean value. The total operational cost of the system is minimized in order to determine the optimal value of N.

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Section: Introductionmentioning

confidence: 99%

Optimal N-Policy for Bernoulli feedback Mx/G/1 Machining System

Varshney¹,

Singh²

2019

IJRAT

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“…In crisp environments, many articles on this topic have been published (for example, [3][4][5][6][7]). Most of the related studies are based on traditional queueing theory, in that the interarrival times and service times are assumed to follow certain probability distributions.…”

Section: Introductionmentioning

confidence: 99%

A bulk arrival queueing model with fuzzy parameters and varying batch sizes

Chen¹

2006

Applied Mathematical Modelling

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This paper develops a nonlinear programming approach to derive the membership functions of the steady-state performance measures in bulk arrival queueing systems with varying batch sizes, in that the arrival rate and service rate are fuzzy numbers. The basic idea is based on ZadehÕs extension principle. Two pairs of mixed integer nonlinear programs (MINLP) with binary variables are formulated to calculate the upper and lower bounds of the system performance measure at possibility level a. From different values of a, the membership function of the system performance measure is constructed. For practice use, the defuzzification of performance measures is also provided via Yager ranking index. To demonstrate the validity of the proposed method, a numerical example is solved successfully.

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“…To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. VALUETOOLS '06 October [11][12][13]2006, Pisa, Italy Copyright 2006 ACM 1-59593-504-5 discrete-time queues stems from their applications in the performance analysis of Broadband Integrated Services Digital Network (BISDN), Asynchronous Transfer Mode (ATM) and related computer communication technologies in which the continuous-time models do not adapt. Reference works on discrete-time queueing theory include the monographs [3,14,16].…”

Section: Introductionmentioning

confidence: 99%

“…This new rule was called early setup under (m, N )-policy. Thereafter, several authors extended the work [10] combining batch arrivals, server vacations and unreliable server [9,11,12].…”

Section: Introductionmentioning

confidence: 99%

Analysis and optimal control of a discrete-time queueing system under the (m,N)-policy

Hernández-Díaz

Moreno

2006

Proceedings of the 1st International Conference on Performance Evaluation Methodolgies and Tools - Valuetools '06

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This paper analyzes a discrete-time single-server queue under bilevel threshold control and early setup. The joint generating function of the server state and the number of customers in the system together with the main performance measures are derived. We also study the length of the different busy periods of the server as well as the number of customers served during a busy period. We establish a cost model and find the optimal solution using a tabu search algorithm due the difficulty to prove the convexity of the cost function. Finally, we show some numerical examples to see the influence of the setup time distribution and the sensibility of the different costs.

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Queue length and waiting time analysis of a batch arrival queue with bilevel control

Cited by 13 publications

References 3 publications

Optimal N-Policy for Bernoulli feedback Mx/G/1 Machining System

Optimal N-Policy for Bernoulli feedback Mx/G/1 Machining System

A bulk arrival queueing model with fuzzy parameters and varying batch sizes

Analysis and optimal control of a discrete-time queueing system under the (m,N)-policy

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