A monotonicity result for a single-server queue subject to a Markov-modulated Poisson process

被引:8
作者
Du, Q
机构
关键词
Poisson arrivals process; zero buffer;
D O I
10.2307/3215223
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Consider a single-server queue with zero buffer. The arrival process is a three-level Markov modulated Poisson process with an arbitrary transition matrix. The time the system remains at level i (i=1, 2, 3) is exponentially distributed with rate c alpha(i) The arrival rate at level i is lambda(i) and the service time is exponentially distributed with rate mu(i). In this paper we first derive an explicit formula for the loss probability and then prove that it is decreasing in the parameter c. This proves a conjecture of Ross and Rolski's for a single-server queue with zero buffer.
引用
收藏
页码:1103 / 1111
页数:9
相关论文
共 12 条
[1]  
CHAN SYW, 1991, ANDROLOGIA, V23, P213
[2]  
CHANG CS, 1991, IBM75593 RES REP
[3]  
FIEDLER M, 1986, SPECIAL MATRICES APP
[4]   HETEROGENEOUS ARRIVAL AND SERVICE QUEUING LOSS MODEL [J].
FOND, S ;
ROSS, SM .
NAVAL RESEARCH LOGISTICS, 1978, 25 (03) :483-488
[5]   ON ROSS CONJECTURES ABOUT QUEUES WITH NONSTATIONARY POISSON ARRIVALS [J].
HEYMAN, DP .
JOURNAL OF APPLIED PROBABILITY, 1982, 19 (01) :245-249
[6]   A SINGLE-SERVER QUEUING LOSS MODEL WITH HETEROGENEOUS ARRIVAL AND SERVICE [J].
NIU, SC .
OPERATIONS RESEARCH, 1980, 28 (03) :584-593
[7]   QUEUES WITH NONSTATIONARY INPUTS [J].
ROLSKI, T .
MATHEMATICAL THEORY OF QUEUEING SYSTEMS, 1989, 5 :113-130
[8]  
ROLSKI T, 1984, LECTURE NOTES CONTRO, V60, P42
[9]   AVERAGE DELAY IN QUEUES WITH NONSTATIONARY POISSON ARRIVALS [J].
ROSS, SM .
JOURNAL OF APPLIED PROBABILITY, 1978, 15 (03) :602-609
[10]  
SVORONOS A, 1987, NAV RES LOG, V34, P579, DOI 10.1002/1520-6750(198708)34:4<579::AID-NAV3220340410>3.0.CO