In this paper, the fluid model with two types of parallel customers and fault delay repair is economically analyzed. The normal working state, fault delay repair state and fault repair state are alternately carried out. When the fluid reaches the system, the net benefit based on the obtained information is calculated, and then whether to enter the system is determined. In the case of complete feasibility and almost visibility, the fluid equilibrium balking strategies and the social benefit optimal strategy per unit time are discussed respectively. Numerical examples are given to analyze the influence of the arrival rate and service rate on average social benefits per unit time.
WANG Jing
,
XU Xiuli
. Equilibrium analysis of the fluid model with two types of parallel customers and delayed repair[J]. Operations Research Transactions, 2026
, 30(1)
: 156
-170
.
DOI: 10.15960/j.cnki.issn.1007-6093.2026.01.010
[1] Economou A, Kanta S. Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs [J]. Operations Research Letters, 2008, 36(6): 696-699.
[2] Li L, Wang J, Zhang F. Equilibrium customer strategies in markovian queues with partial breakdowns [J]. Computers & Industrial Engineering, 2013, 66(4): 751-757.
[3] Yu S, Liu Z, Wu J. Strategic behavior in the partially observable markovian queues with partial breakdowns [J]. Operations Research Letters, 2017, 45(5): 471-474.
[4] Xu B, Xu X. Equilibrium strategic behavior of customers in the M/M/1 queue with partial failures and repairs [J]. Operational Research, 2018, 18(2): 273-292.
[5] Balachandran K. Purchasing priorities in queues [J]. Management Science, 1972, 18(5): 319- 326.
[6] Xu B, Xu X, Wang X. Optimal balking strategies for high-priority customers in M/G/1 queues with 2 classes of customers [J]. Journal of Applied Mathematics and Computing, 2016, 51(1): 623-642.
[7] 张淞钛，徐秀丽.具有两类平行顾客的不完全故障排队系统均衡分析[J].系统科学与数学，2019， 39(4):637-647.
[8] Anick D, Mitra D, Sondhi M. Stochastic theory of a data-handling system with multiple sources [J]. Bell Labs Technical Journal, 1982, 61(8): 1871-1894.
[9] Xu X, Wang H. Analysis of fluid model modulated by an M/PH/1 working vacation queue [J]. Journal of Systems Science and Systems Engineering, 2019, 28(2): 132-140.
[10] Yu S, Liu Z, Wu J. Fluid queue driven by a multi-server queue with multiple vacations and vacation interruption [J]. RAIRO-Operations Research, 2017, 51(4): 931-944.
[11] 徐秀丽，宋晓凤，靖欣，等.PH/M/1排队系统驱动的流模型[J].系统科学与数学，2017，37(3)： 838-845.
[12] Economou A, Manou A. Strategic behavior in an observable fluid queue with an alternating service process [J]. European Journal of Operational Research, 2016, 254(1): 148-160.
[13] Wang S, Xu X. Equilibrium strategies of the fluid queue with working vacation [J]. Operational Research, 2021, 21(2): 1211-1228.
[14] Liu J, Xu X, Wang S, et al. Equilibrium analysis of the fluid model with two types of parallel customers and breakdowns [J]. Communications in Statistics-Theory and Methods, 2021, 50(24): 5792-5805.
