Computing steady state probabilities in lambda(n)/G/1/K queue

被引:12
作者
Gupta, UC
Rao, TSSS
机构
[1] Department of Mathematics, Indian Institute of Technology
[2] Banaras Hindu University, Varanasi
[3] Indian Institute of Technology, Delhi
[4] Department of Mathematics, Indian Institute of Technology, Kharagpur
[5] Royal Military College of Canada, Kingston, Ont.
[6] Indian Institute of Technology, Kharagpur
[7] Department of Mathematics, I.I.T., Kharagpur
关键词
queueing; computational analysis; state-dependent arrival; general service time; queue length distribution;
D O I
10.1016/0166-5316(94)00035-2
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper a recursive method is developed to obtain the steady state probability distribution of the number in system at arbitrary and departure time epochs of a single server state-dependent arrival rate queue lambda(n)/G/1/K in which the arrival process is Markovian with arrival rates lambda(n) which depend on the number of customers n in the system and general service time distribution. It is assumed that there exists an integer K such that lambda(n)>0 for all 0 less than or equal to n < K and lambda(n) = 0 for all n greater than or equal to K. Numerical results have been presented for many queueing models by suitably defining the function lambda(n). These include machine interference model, queues with balking, queues with finite waiting space and machine interference model with finite waiting space. These models have wide application in computer/communication networks.
引用
收藏
页码:265 / 275
页数:11
相关论文
共 15 条
[1]   THE MX G 1 QUEUE WITH FINITE WAITING ROOM [J].
BABA, Y .
JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF JAPAN, 1984, 27 (03) :260-272
[2]  
Carmichael D.G., 1987, ENG QUEUES CONSTRUCT
[3]   ON EXACT COMPUTATIONAL ANALYSIS OF DISTRIBUTIONS OF NUMBERS IN SYSTEMS FOR M/G/1/N + 1 AND GI/M/1/N + 1 QUEUES USING ROOTS [J].
CHAUDHRY, ML ;
GUPTA, UC ;
AGARWAL, M .
COMPUTERS & OPERATIONS RESEARCH, 1991, 18 (08) :679-694
[4]   SINGLE-SERVER FINITE QUEUING MODEL WITH STATE-DEPENDENT ARRIVAL AND SERVICE PROCESSES [J].
COURTOIS, PJ ;
GEORGES, J .
OPERATIONS RESEARCH, 1971, 19 (02) :424-&
[5]  
Gong W.-B., 1992, COMM STAT STOCHASTIC, V8, P733
[6]  
GUPTA UC, 1995, EUR J OPER RES, V89, P164
[7]   SOLUTION OF QUEUING PROBLEMS BY A RECURSIVE TECHNIQUE [J].
HERZOG, U ;
WOO, L ;
CHANDY, KM .
IBM JOURNAL OF RESEARCH AND DEVELOPMENT, 1975, 19 (03) :295-300
[8]   STEADY-STATE PROBABILITIES FOR A QUEUE WITH A GENERAL SERVICE DISTRIBUTION AND STATE-DEPENDENT ARRIVALS [J].
MARIE, RA ;
PELLAUMAIL, JM .
IEEE TRANSACTIONS ON SOFTWARE ENGINEERING, 1983, 9 (01) :109-113
[9]  
MARIE RA, 1980, P PERF 80 TOR, P117
[10]   ON A CLASS OF QUEUING PROBLEMS AND DISCRETE TRANSFORMS [J].
RAO, SS ;
JAISWAL, NK .
OPERATIONS RESEARCH, 1969, 17 (06) :1062-&