An Approximation of the Customer Waiting Time for Online Restaurants Owning Delivery System

  • Tianhua Zhang
  • Fu ZhaoEmail author
  • Juliang Zhang
  • Gamini Mendis
  • Yihong Ru
  • John W. Sutherladn


Online restaurants, which receive online orders and deliver food directly to the customer’s residence, are becoming increasingly popular. To be successful, online restaurants need to provide reliable and prompt deliveries. Careful design of the meal preparation and order delivery systems is needed to avoid excessive customer waiting time between ordering and delivery. This paper considers the meal preparation and delivery processes simultaneously to approximate average customer waiting time for deliveries. The authors first discuss the system performance with one cook and unit-capacity delivery vehicles, using an M/G/1 queue and a GI/G/1 queue. Numerical experiments show that our approximation can adequately describe real waiting times. Then, series queues with multiple cooks and multi-capacity delivery vehicles, e.g., an M/G/n queue and a GI/Gn/1 queue, are examined. Results show that except for situations with a large meal preparation time and a small vehicle capacity, compared with the result of simulation, the approximation in this paper is acceptable with a deviation of less than 20%. The marginal decrease in waiting time associated with hiring more vehicles is estimated under different meal preparation speeds, sizes of service area and vehicle capacities.


Delivery electronic commerce last mile problem online restaurant queuing theory 


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Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Tianhua Zhang
    • 1
  • Fu Zhao
    • 2
    Email author
  • Juliang Zhang
    • 1
  • Gamini Mendis
    • 3
  • Yihong Ru
    • 1
  • John W. Sutherladn
    • 3
  1. 1.School of Economics and ManagementBeijing Jiaotong UniversityBeijingChina
  2. 2.School of Mechanical EngineeringPurdue UniversityWest LafayetteUSA
  3. 3.Division of Environmental and Ecological EngineeringPurdue UniversityWest LafayetteUSA

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