基于MPEWMA控制图的串联排队网络的监测与控制

doi:10.6040/j.issn.1671-9352.0.2021.786

Abstract

Abstract:

We constructed a multivariate Poisson exponential weighted moving average (MPEWMA) chart, which can detect a series queuing network with intermediate inputs. The MPEWMA chart can be used to monitor and control multiple nodes in the system simultaneously. We detect the change points of the external arrival rate λ_iby the MPEWMA chart, segment the process according to the change points, and estimate the segmented parameters using the MLE method when each segment meets the stationarity of each segment. Under the constraint of the lowest cost, the estimated value of the arrival rate γ_i is calculated from external inputs λ_i, and the service process is optimized in a timely manner based on changes in the arrival rate. The service rate is adjusted reasonably to reduce customer waiting time. The random simulation results indicate that when the customer's arrival rate changes, the MPEWMA chart can timely detect changes in external arrival rate λ_i and issue alerts, playing an important role in the smooth operation of the queuing system.

Key words: tandem queuing network, MPEWMA chart, change point detection, system optimization

CLC Number:

O211.9

Qi GAO,Hongshuai DAI,Yanhua WU. MPEWMA chart for detecting tandem queuing network[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 104-110, 117.

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References 19

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位移	[0,0]	[0,1]	[1,1]	[0,2]	[2,1]	[2,2]	[1,3]	[2,3]	[3,3]	[3,4]	[4,4]
δ	0	0.41	0.65	0.75	0.98	1.17	1.17	1.39	1.62	1.81	2.01
r=0.05 H=7.52	200.12	33.02	17.85	14.27	10.23	8.22	8.16	6.62	5.46	4.75	4.15
r=0.1 H=8.77	199.94	36.54	17.65	13.78	9.21	7.19	7.12	5.61	4.50	3.87	3.33
r=0.2 H=9.87	198.423	46.29	20.69	15.68	9.57	6.96	6.92	5.17	3.97	3.29	2.76

	λ_1i	λ_i2
节点1	3.044	2.923
节点2	5.238	5.964

	最优服务率μ^*	平均等待时间W_S^E	最优成本z
γ₂₁=5.24	9.28	0.139	105.24
γ₂₂=11.20	19.88	0.065	211.66

	最优服务率μ^*	平均等待时间EWs	最优成本z
γ₂₁=15.39	27.96	0.044	875.42
γ₂₁=17.02	30.92	0.039	964.25

MPEWMA chart for detecting tandem queuing network

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