Article Contents
Article Contents

# Algorithmic computation of MAP/PH/1 queue with finite system capacity and two-stage vacations

• * Corresponding author: Qingqing Ye

The first author is supported by Natural Science Foundation of Jiangsu Province (grant Nos. BK20180783, 18KJB110021), and The Startup Foundation for Introducing Talent of Nanjing University of Information Science and Technology(grant No. 2017r082)

• In this article, we study a discrete-time MAP/PH/1 queue with finite system capacity and two-stage vacations. The two-stage vacations policy which comprises single working vacation and multiple vacations is featured by that once the system is empty during the regular busy period, the system first takes the working vacation during which the server can still provide the service but at a lower service rate. After this working vacation, if the system is empty, the server will take a vacation during which the server stops its service completely, otherwise, the server resumes to the normal service rate. For this queue, using the matrix-geometric combination solution method, we obtain the stationary probability vectors when the traffic intensity is not equal to one. In addition, we discuss the spectrum properties of the key matrices and give their decomposition results that can be used to reduce the computation loads. Further, waiting time is derived by constructing an absorbing Markov chain. Various performance measures are obtained. At last, some numerical examples are presented to show the impacts of system parameters on performance measures.

Mathematics Subject Classification: Primary: 60K25; Secondary: 68M20.

 Citation:

• Figure 1.  Schematic representation

Figure 2.  E(L) versus N

Figure 3.  Pempty versus N

Figure 4.  Pfull versus N

Figure 5.  PW versus N

Figure 6.  PV versus N

Figure 7.  PB versus N

Figure 8.  Ploss versus N

Figure 9.  lg (Ploss) versus N

Figure 10.  E(L) versus N

Figure 11.  Pempty versus N

Figure 12.  Pfull versus N

Figure 13.  PW versus N

Figure 14.  PV versus N

Figure 15.  PB versus N

Figure 16.  Ploss versus N

Figure 17.  lg(Ploss) versus N

Figure 18.  ρ < 1

Figure 19.  ρ > 1

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