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IJSTR >> Volume 8 - Issue 8, August 2019 Edition

International Journal of Scientific & Technology Research  
International Journal of Scientific & Technology Research

Website: http://www.ijstr.org

ISSN 2277-8616

Application Of Queuing Theory On A Food Chain

[Full Text]



Abhishek Yadav , Dr. Nagendra Sohani



arrival rate, customer satisfaction, m/m/1 queuing model, multi-server queuing model, queuing theory, service time, waiting time.



In their daily life people go to many places such as hotels, hospitals, banks etc. to avail some kinds of services and the biggest problem that they face there is the formation of long queues and high waiting time. It affects customer in a negative way and harms the growth of business. To grow in today's competitive market a firm always need to improve its services and should focus on satisfying customer’s needs in best possible way and apply a strategy that suits the firm. To pursue quality education students living out of station depends on food services for their food requirement and as the population of students is very high it causes load on food chains and they always run out of capacity and often fails to provide a quality service. This paper studies and evaluates queuing system and operating characteristics of a food chain by applying queuing theory. It focuses on queuing modeling of the system and finding ways to improve service and reduce waiting time by calculating arrival, departure, queue length etc. It also aims at finding a balance between cost of providing service and loss due to high waiting time, so that system can operate at an optimized minimum possible cost. The study shows that the food chain needs to increase seating capacity and instead of the current m/m/1 queuing model, a multi-server model will best suit the food chain. The study also consists of a survey to find potential customers that can join the food chain if waiting time of the system decreases. The survey also aims to find problems in the food chain that are the reasons behind high waiting time and eliminate them.



[1] Mor Armony, Shlomo Israelit, Avishai Mandelbaum, Yariv N. Marmor, Yulia Tseytlin, Galit B. Yom-Tov (2015) On Patient Flow in Hospitals: A Data-Based Queueing-Science Perspective. Stochastic Systems 5(1):146-194.
[2] A. Gal, Traveling time prediction in scheduled transportation with journey segments, Information system (2015),
[3] Ugwa Magnus, Okonkwo Chukwudi Joseph, Okonkwo Ifeanyi Anthony(2015), The application of queuing theory in the effective management of time in money deposit banks - A study of Zenith bank PLC in Enugu Metropolis.
[4] Oyatoye E.O., Adebiyi, Sulaimon Olanrewaju, Okoye John Chinweze, Amole Bilqis Bolanle (2011) Application of Queueing theory to port congestion problem in Nigeria:24-36.
[5] Dr. Nagendra Sohani, Rahul Chakrawarti (2015) Performance evaluation: By analyzing food chain of Akshay Patra:41-43.
[6] Aksin, O. Z., Karaesmen, F. and Ormeci, E. L. (2007). A Review of Workforce CrossTraining in Call Centers from an Operations Management Perspective. In Workforce Cross Training Handbook (D. Nembhard, ed.), CRC Press.
[7] Allon, G., Bassamboo, A. and Gurvich, I. (2011). “We Will Be Right with You”: Managing Customer Expectations with Vague Promises and Cheap Talk. Operations Research 59 1382–1394. MR2872007
[8] Armony, M. (2005). Dynamic Routing in Large-Scale Service Systems with Heterogeneous Servers. Queueing Systems 51 287–329. MR2189596
[9] Armony, M., Chan, C. W. and Zhu, B. (2013). Critical Care in Hospitals: When to Introduce a Step Down Unit? Working paper, Columbia University.
[10] Armony, M. and Ward, A. (2010). Fair Dynamic Routing in Large-Scale HeterogeneousServer Systems. Operations Research 58 624–637. MR2680568
[11] Armony, M., Israelit, S., Mandelbaum, A., Marmor, Y. N., Tseytlin, Y. and YomTov, G. B. (2015). On Patient Flow in Hospitals: A Data-Based Queueing-Science Perspective. An Extended Version (EV). Working paper, http://ie.technion.ac.il/ serveng/References/Patient%20flow%20main.pdf.
[12] Atar, R., Mandelbaum, A. and Zviran, A. (2012). Control of Fork-Join Networks in Heavy Traffic. Allerton Conference.
[13] Atar, R. and Shwartz, A. (2008). Efficient Routing in Heavy Traffic under Partial Sampling of Service Times. Mathematics of Operations Research 33 899–909. MR2464649
[14] Balasubramanian, H., Muriel, A. and Wang, L. (2012). The Impact of Flexibility and Capacity Allocation on the Performance of Primary Care Practices. Flexible Services and Manufacturing Journal 24 422–447.
[15] Balasubramanian, H., Banerjee, R., Denton, B., Naessens, J., Wood, D. and Stahl, J. (2010). Improving Clinical Access and Continuity Using Physician Panel RSSedesign. Journal of General Internal Medicine 25 1109–1115.
[16] Barak-Corren, Y., Israelit, S. and Reis, B. Y. (2013). Progressive Prediction of Hospitalization in The Emergency Department: Uncovering Hidden Patterns to Improve Patient Flow. Working paper.
[17] Baron, O., Berman, O., Krass, D. and Wang, J. (2014). Using Strategic Idleness to Improve Customer Service Experience in Service Networks. Operations Research 62 123–140. MR3188591
[18] W. van der Aalst, Process Mining: Discovery, Conformance and Enhancement of Business Processes, Springer, 2011.
[19] A. Senderovich, M. Weidlich, A. Gal, A. Mandelbaum, Mining resource scheduling protocols, in: BPM, Vol. 8659 of LNCS, Springer, 2014, pp. 200–216.
[20] W. Whitt, Stochastic-process limits: an introduction to stochastic-process limits and their application to queues, Springer, 2002.
[21] R. Ibrahim, W. Whitt, Real-time delay estimation based on delay history, Manufacturing and Service Operations Management 11 (3) (2009) 397– 415.
[22] M. I. Reiman, B. Simon, A network of priority queues in heavy traffic: One bottleneck station, Queueing Systems 6 (1) (1990) 33–57.
[23] L. Breiman, J. Friedman, R. Olshen, C. Stone, Classification and regression trees, Wadsworth International (1984).
[24] L. Breiman, Bagging predictors, Machine learning 24 (2) (1996) 123–140.
[25] L. Breiman, Random forests, Machine learning 45 (1) (2001) 5–32.
[26] P. Geurts, D. Ernst, L. Wehenkel, Extremely randomized trees, Machine Learning 63 (1) (2006) 3–42.
[27] H. Drucker, Improving regressors using boosting techniques, in: ICML, Vol. 97, 1997, pp. 107–115.
[28] J. H. Friedman, Greedy function approximation: a gradient boosting machine, Annals of Statistics (2001) 1189–1232.
[29] F. Pedregosa, G. Varoquaux, A. Gramfort, V. Michel, B. Thirion, O. Grisel, M. Blondel, P. Prettenhofer, R. Weiss, V. Dubourg, J. Vanderplas, A. Passos, D. Cournapeau, M. Brucher, M. Perrot, E. Duchesnay, Scikit-learn: Machine learning in Python, Journal of Machine Learning Research 12 (2011) 2825–2830.
[30] T. Hastie, R. Tibshirani, J. Friedman, The Elements of Statistical Learning, Springer Series in Statistics, Springer New York Inc., 2001.
[31] B. McCann, A review of scats operation and deployment in Dublin.
[32] Ibrahim, R. and Whitt, W. (2011). Wait-Time Predictors for Customer Service Systems with Time-Varying Demand and Capacity. Operations Research 59 1106–1118. MR2864327
[33] IHI (2011). Patient First: Efficient Patient Flow Management Impact on the ED. Institute for Healthcare Improvement. http://www.ihi.org/knowledge/Pages/ ImprovementStories/PatientFirstEfficientPatientFlowManagementED.aspx.
[34] Janssen, A. J. E. M., van Leeuwaarden, J. S. H. and Zwart, B. (2011). Refining Square-Root Safety Staffing by Expanding Erlang C. Operations Research 56 1512– 1522. MR2872017 JCAHO (2004).
[35] JCAHO Requirement: New Leadership Standard on Managing Patient Flow for Hospitals. Joint Commission Perspectives 24 13–14.
[36] Jennings, O. B. and de V´ericourt, F. (2008). Dimensioning Large-Scale Membership Services. Operations Research 56 173–187. MR2402225
[37] Jennings, O. B. and de V´ericourt, F. (2011). Nurse Staffing in Medical Units: A Queueing Perspective. Operations Research 59 1320–1331. MR2872002
[38] Jouini, O., Dallery, Y. and Aksin, O. Z. (2009). Queueing Models for Full-Flexible Multi-class Call Centers with Real-Time Anticipated Delays. International Journal of Production Economics 120 389–399.
[39] Kaplan, R. S. and Porter, M. E. (2011). How to Solve the Cost Crisis in Health Care. Harvard Business Review 89 46–64.
[40] Kc, D. and Terwiesch, C. (2009). Impact of Workload on Service Time and Patient Safety: An Econometric Analysis of Hospital Operations. Management Science 55 1486– 1498.
[41] Kelly, F. P. (1979). Markov Processes and Reversibility. Wiley.
[42] https://www.isixsigma.com/wp-content/uploads/images/stories/Sherman%206-28/0726_SHERMAN.gif
[43] Kim, S. H. and Whitt, W. (2014). Are Call Center and Hospital Arrivals Well Modeled by Nonhomogeneous Poisson Processes? M&SOM 16 464–480.
[44] Koc¸ aga, Y.L., Armony, M. and Ward, A. R. (2015). Staffing Call Centers with Uncertain Arrival Rates and Co-sourcing. Production and Operations Management n/a– n/a.
[45] Leite, S. C. and Fragoso, M. D. (2013). Diffusion Approximation for Signaling Stochastic Networks. Stochastic Processes and their Applications 123 2957–2982. MR3062432.
[46] Long, E. F. and Mathews, K. M. (2012). “Patients without Patience”: A Priority Queuing Simulation Model of the Intensive Care Unit. Working paper.
[47] Maa, J. (2011). The Waits that Matter. The New England Journal of Medicine 364 2279–2281.
[48] Maman, S. (2009). Uncertainty in the Demand for Service: The Case of Call Centers and Emergency Departments. Master’s thesis, Technion—Israel Institute of Technology.
[49] Maman, S., Zeltyn, S. and Mandelbaum, A. (2011). Uncertainty in the Demand for Service: The Case of Call Centers and Emergency Departments. Working paper.