Improving efficiency of the queueing system with two types of customers by service decomposition

Linhong Li; Wei Xu; Zhen Wang; Liwei Liu; Linhong Li; Wei Xu; Zhen Wang; Liwei Liu

doi:10.3934/math.20231295

AIMS Mathematics

2023, Volume 8, Issue 11: 25382-25408. doi: 10.3934/math.20231295

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Research article

Improving efficiency of the queueing system with two types of customers by service decomposition

1.
School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China
2.
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China

Received: 05 June 2023 Revised: 16 August 2023 Accepted: 24 August 2023 Published: 31 August 2023
MSC : 60K25, 68M20, 90B05

The economic improvements of a queueing system with two types of customers achieved by service decomposition are examined. The service process for a Type 2 customer can be split into two phases: a basic service and an additional service. The basic service rate is equal to that of the Type 1 customer. Additional services can be viewed as orders stored in inventory and processed when the server is idle. Once a new customer arrives during idle time, the server will provide a basic service to the customer upon his/her arrival. That is, customers have preemptive priority for orders stored in inventory. We obtain a two-dimensional unbounded Markov process and apply the multivariate generating function to derive the stationary probability of the proposed model as well as some performance measures. The condition under which performing service decomposition can improve economic efficiency is also obtained. Both the optimal inventory capacity and the minimum system cost are obtained numerically. Numerical experiments demonstrate the impact of optimal inventory setting on economic improvement efficiency. Finally, simulation experiments prove the correctness of our theoretical analysis.
- queueing-inventory system,
- service decomposition,
- economic improvement,
- two types of customers
Citation: Linhong Li, Wei Xu, Zhen Wang, Liwei Liu. Improving efficiency of the queueing system with two types of customers by service decomposition[J]. AIMS Mathematics, 2023, 8(11): 25382-25408. doi: 10.3934/math.20231295

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Abstract

The economic improvements of a queueing system with two types of customers achieved by service decomposition are examined. The service process for a Type 2 customer can be split into two phases: a basic service and an additional service. The basic service rate is equal to that of the Type 1 customer. Additional services can be viewed as orders stored in inventory and processed when the server is idle. Once a new customer arrives during idle time, the server will provide a basic service to the customer upon his/her arrival. That is, customers have preemptive priority for orders stored in inventory. We obtain a two-dimensional unbounded Markov process and apply the multivariate generating function to derive the stationary probability of the proposed model as well as some performance measures. The condition under which performing service decomposition can improve economic efficiency is also obtained. Both the optimal inventory capacity and the minimum system cost are obtained numerically. Numerical experiments demonstrate the impact of optimal inventory setting on economic improvement efficiency. Finally, simulation experiments prove the correctness of our theoretical analysis.

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