Supermarket Application Based on Queueing Theory

In order to better reduce the operation cost of Beidaihe small supermarket, especially the reasonable arrangement of the cashier of a number, we can use the queueing theory to solve this question. Queueing theory is the theory of random service system, ba

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Supermarket Application Based on Queueing Theory Tongjuan Zhao and Chunhui He

Abstract In order to better reduce the operation cost of Beidaihe small supermarket, especially the reasonable arrangement of the cashier of a number, we can use the queueing theory to solve this question. Queueing theory is the theory of random service system, based on the service object and the arrival of business hours of the statistical study, draws some quantitative indices (waiting time, queue length, busy period length) statistical regularity. Supermarket operators in order to facilitate the purchase installed large number of tourists pay POS machine, to reduce the customer waiting time. Introduction of excess POS will increase the cost of the supermarket operators. Use queue theory by comparing the calculated cash and credit card payment waiting time. With the results of guided supermarket operator reasonable arrangement of POS machine number. Keywords Queueing theory

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67.1 Introduction Queueing theory (queueing theory), or the theory of random service system, is based on the service object and the arrival of business hours of the statistical study; the quantitative index (waiting time, queue length, busy period length) statistical regularity, then according to these rules to improve the service system structure or organization is service object, makes the service system that cannot only meet the

T. Zhao (&)  C. He Department of Basic Courses, Qinhuangdao Institute of Technology, Qinhuangdao 066100, China e-mail: [email protected]

Z. Zhong (ed.), Proceedings of the International Conference on Information Engineering and Applications (IEA) 2012, Lecture Notes in Electrical Engineering 218, DOI: 10.1007/978-1-4471-4847-0_67, Ó Springer-Verlag London 2013

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needs of the service object, and can make the body of the economic cost or certain indices [1]. Queueing system comprises three components: input process, queueing rules, and service agencies. A queueing system can be described as: customer service to seek, if there are customer arrivals, not immediately enter the service, need to wait, accept service, after leaving the system [2, 3]. In people’s daily life, especially in modern urban life, queueing phenomenon is everywhere. For example, go to a hospital or the railway station service window, often had to wait in line, the plane circled in the air, not landing, the aircraft in the waiting ‘‘queue’’, all according to a certain order and pattern of landing. The finite sex of resource and demand randomness is queueing phenomenon based. Increased resources, such as increasing the service window, setting more runways, site equipment capacity, can reduce customer queueing phenomenon, even may not line up. But when fewer customers, inevitable meeting causes resources unused, results equivalent to resources in ‘‘queuing’’ waiting for customers to visit [4]. Therefore, to increase the service mechanism, can certainly reduce queueing phenomenon, but increase the cost of service; conversely,