The M/M/1 queue with mass exodus and mass arrivals when empty

Journal of Applied Probability

Volumn 34, Issue 1, 1997, Pages 192-207

  Chen, Anyue ^a   Renshaw, Eric ^b  

^a UNIVERSITY OF GREENWICH   (United Kingdom)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

Catastrophe; Equilibrium probabilities; Factorial moments; Idle probability; M M 1 queue; Mass immigration; Q Process; Recurrence; Transience

Indexed keywords

OPERATIONS RESEARCH; PROBABILITY; RANDOM PROCESSES; STATISTICAL METHODS;

EQUILIBRIUM PROBABILITY; FACTORIAL MOMENT; IDLE PROBABILITY; MASS IMMIGRATION; POSITIVE RECURRENCE;

QUEUEING THEORY;

EID: 0031082711     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200100816     Document Type: Article

References (17)

1. ABRAMOWITZ, M. AND STEGUN, A. I. (1965) Handbook of Mathematical Functions. Dover, New York.
2. ANDERSON, W. J. (1991) Continuous Time Markov Chains. Springer, Berlin.
3. ASMUSSEN, S. (1987) Applied Probability and Queues. Wiley, New York.
4. CHEN, A. Y. AND RENSHAW, E. (1990) Markov branching processes with instantaneous immigration. Prob. Theory Rel. Fields 87, 209-240.
5. CHEN, A. Y. AND RENSHAW, E. (1993a) Existence and uniqueness criteria for conservative uni-instantaneous denumerable Markov processes. Prob. Theory Rel. Fields 94, 427-456.
6. CHEN, A. Y. AND RENSHAW, E. (1993b) Recurrence of Markov branching processes with immigration. Stoch. Proc. Appl. 45, 231-242.
7. CHEN, A. Y. AND RENSHAW, E. (1995) Markov branching processes regulated by large immigration and emigration. Stoch. Proc. Appl. 57, 339-359.
8. COX, D. R. AND MILLER, H. D. (1965) Theory of Stochastic Processes. Methuen, London.
9. GROSS, D. AND HARRIS, C. M. (1985) Fundamentals of Queuing Theory. Wiley, New York.
10. HOU, Z. T. AND GUO, Q. F. (1988) Homogeneous Denumerable Markov Processes. Springer, Berlin.
11. KLEINROCK, I. (1975) Queueing Systems. Vol. 1. Wiley, New York.
12. PARTHASARATHY, P. R. AND KRISHNA KUMAR, B. (1991) Density-dependent birth and death process with state-dependent immigration. Math. Comput. Modelling 15, 11-16.
13. RENSHAW, E. AND CHEN, A. Y. (1996) Birth-death processes with mass annihilation and state-dependent immigration. Stoch. Models (to appear).
14. SAATY, T. L. (1961) Elements of Queueing Theory. McGraw Hill, New York.
15. SHARMA, O. P. (1990) Markovian Queues. Ellis Horwood, New York.
16. WANG, T. K. AND YANG, X. Q. (1992) Birth and Death Processes and Markov Chains. Springer, Berlin.
17. YANG, W. Q. (1990) The Construction Theory of Denumerable Markov Processes. Wiley, New York.