Analysis of Multiple Working Vacations Queuing System With Encouraged Arrival Using M/M (a,b)/1 Model

Authors

  • prakati P Department of Mathematics, Nirmala College for Women, Bharathiar University, Coimbatore, India. https://orcid.org/0009-0006-3197-3210
  • Rose Mary K. Julia Department of Mathematics, Nirmala College for Women, Bharathiar University, Coimbatore, India.

DOI:

https://doi.org/10.21123/bsj.2024.9162

Keywords:

Encouraged arrival, Expected Queue Length, General Bulk Service Rule, Multiple Working Vacations, Queuing Model

Abstract

Generally, it is very common in our daily life to meet up with queuing systems. This study examines the concept of encouraged arrival in M/M (a,b)/1/Multiple Working Vacations queuing model that follows the General Bulk Service Rule. The considered queuing model consists of three states namely idle, working vacation and regular busy period. The single server available in the system usually goes on vacation whenever the system is idle, that is, when it is empty. This model deals with multiple working vacations of the server which are exponentially distributed and the concept of encouraged arrival of the customers is examined particularly in the regular busy period. Specifically, the term encouraged arrival is a recent addition to the queue with the existing customers following Poisson distribution and are served in batches. The main objective of the study is to calculate the mean queue length (Lq) and various other performance measures of the discussed queuing model. Moreover, a real life application of the studied model has been implemented in a case study and the expected queue length has been discussed.

References

Aarthi S, Shanmugasundari M. Comparison of single server queuing performance measures using fuzzy queuing models and intuitionistic fuzzy queuing models with infinite capacity. J Intell Fuzzy Syst. 2022; 44(3): 4733-4746. https://doi.org/10.3233/JIFS-221367.

Abdelmawgoud MTA, Dawood AAA, Moussa MHB. The Impact of Prolonged Waiting Time of Food Service on Customers’ Satisfaction. Minia J Tour Hosp Res. 2016; 1(1): 247-251.

Abid NA, Al-Madi AK. On The Queuing System M/Er/1/N. Baghdad Sci J. 2012; 9(2): 367-371. https://doi.org/10.21123/bsj.9.2.367-371

Ibraheem NA, Hasan MM. Combining Several Substitution Cipher Algorithms using Circular Queue Data Structure. Baghdad Sci J. 2020; 17(4): 1320-1320. https://doi.org/10.21123/bsj.2020.17.4.1320

Julia Rose Mary K, Afthab Begum M, Jemila Parveen M. Bi-level threshold policy of Mx/(G1,G2)/1 queue with early setup and single vacation. Int J Oper Res. 2011; 10(4): 469-493. https://doi.org/10.1504/IJOR.2011.039714

Levy Y, Yechiali U. An M/M/S Queue with Servers' Vacations. INFOR Inf Syst Oper Res. 1976; 14(2): 153-163. https://doi.org/10.1080/03155986.1976.11731635

Liu W, Xu X, Tian N. Stochastic decompositions in the M/M/1 queue with working vacations. Oper Res Lett. 2007; 35(5): 595–600. https://doi.org/10.1016/j.orl.2006.12.007

Majid S, Manoharan P, Ashok A. Analysis of an M/M/c Queueing System with Working Vacation and Impatient Customers. International Conference on Current Scenario in Pure and Applied Mathematics (ICCSPAM). Am Int J Res Sci Technol Eng Math. 2019; 314-322.

Malik S, Gupta R. Analysis of Finite Capacity Queueing System with Multiple Vacations and Encouraged Customers. Int J Sci Res Math Stat Sci. 2022; 9(2): 17-22.

Be Moussa MH, Abd Elmawgoud MTA, Elias AN. Measuring Service Time Characteristics in Fast Food Restaurants in Cairo: A Case Study. Tour Today. 2015; 1(15): 90-104.

Neuts MF. A General Class of Bulk Queues with Poisson Input. Ann Math Statist. 1967; 38(3): 759-770. https://doi.org/10.1214/AOMS%2F1177698869

Servi LD, Finn SG. M/M/1 queues with working vacations (M/M/1/WV). Perform. Evaluation. 2002; 50(1): 41-52. https://doi.org/10.1016/S0166-5316(02)00057-3

Som BK, Seth S. An M/M/1/N Encouraged Arrivals Queuing Model with Reverse Reneging. J Eng Math. 2019; 3(2): 1-5.

Lakshmanan K, Padmasekaran S, Jeganathan K. Mathematical Analysis of Queueing-Inventory Model with Compliment and Multiple Working Vacations. Int J Eng Adv Technol. 2019; 8(6): 4239-4240. https://doi.org/10.35940/ijeat.F9003.088619

Srivastava RK, Singh S, Singh A. Bulk Arrival Markovian Queueing System with Two Types of Services and Multiple Vacations. Int J Math Comput Res. 2020; 8(8): 2130-2136. https://doi.org/10.47191/ijmcr/v8i7.04.

Tamrakar GK, Banerjee A. On steady-state joint distribution of an infinite buffer batch service poisson queue with single and multiple vacation. OPSEARCH. 2020; 57(4): 1337–1373. https://doi.org/10.1007/s12597-020-00446-9

Wang J, Abouee-Mehrizi H, Baron O, Berman O. Tandem queues with impatient customers. Perform Evaluation. 2019; 135(1): 102011-102011. https://doi.org/10.1016/j.peva.2019.102011.

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Analysis of Multiple Working Vacations Queuing System With Encouraged Arrival Using M/M (a,b)/1 Model. Baghdad Sci.J [Internet]. [cited 2024 Dec. 4];22(6). Available from: https://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/9162