Monotonicity results for MR/GI/1 queues

Journal of Applied Probability

Volumn 34, Issue 2, 1997, Pages 514-524

  Bäuerle, Nicole ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

Markov renewal queues; Stochastic ordering; Supermodular functions

Indexed keywords

FUNCTIONS; MARKOV PROCESSES; MATHEMATICAL MODELS; MATRIX ALGEBRA;

MARKOV RENEWAL QUEUES; STOCHASTIC ORDERING; SUPERMODULAR FUNCTIONS;

QUEUEING THEORY;

EID: 0031337884     PISSN: 00219002     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0021900200101147     Document Type: Article

References (16)

1. BÄUERLE, N. (1994) Stochastic models with a Markovian environment. PhD dissertation. University of Ulm.
2. CHANG, C., CHAO, X., PINEDO, M. AND SHANTHIKUMAR, J. (1991) Stochastic convexity for multidimensional processes and its application. Adv. Appl. Prob. 23, 210-228.
3. DALEY, D. AND ROLSKI, T. (1992) Finiteness of waiting-time moments in general stationary single-server queues. Ann. Appl. Prob. 2, 987-1008.
4. KAMAE, T. AND KRENGEL, U. (1978) Stochastic partial orderings. Ann. Prob. 6, 1044-1049.
5. KAMAE, T., KRENGEL, U. AND O'BRIEN, G. L. (1977) Stochastic inequalities on partially ordered spaces. Ann. Prob. 5, 899-912.
6. LOYNES, R. (1962) The stability of a queue with non-independent interarrival and service times. Proc. Camb. Phil. Soc. 10, 497-520.
7. MARSHALL, A. AND OLKIN, I. (1979) Inequalities: Theory of Majorization and its Applications. Academic Press, New York.
8. MEESTER, L. AND SHANTHIKUMAR, J. (1993) Regularity of stochastic processes. Prob. Eng. Inf. Sci. 7, 343-360.
9. ROLSKI, T. (1986) Upper bounds for single server queues with doubly stochastic Poisson arrivals. Math. Operat. Res. 11, 442-450.
10. ROLSKI, T. (1989) Queues with nonstationary inputs. Queueing Systems 5, 113-130.
11. SHAKED, M. AND SHANTHIKUMAR, J. (1990) Parametric stochastic convexity and concavity of stochastic processes. Ann. Inst. Statist. Math. 42, 509-531.
12. SHAKED, M. AND SHANTHIKUMAR, J. (1994) Stochastic Orders and Their Applications. Academic Press, New York.
13. STOYAN, D. (1983) Comparison Methods for Queues and Other Stochastic Models. Wiley, Chichester.
14. SZEKLI, R., DISNEY, R. L. AND HUR, S. (1994a) MR/GI/1 queues with positively correlated arrival stream. J. Appl. Prob. 31, 497-514.
15. SZEKLI, R., DISNEY, R. L. AND HUR, S. (1994b) On performance comparison of MR/GI/1 queues. Queueing Systems 17, 451-470.
16. TCHEN, A. (1980) Inequalities for distributions with given marginals. Ann. Prob. 8, 814-827.