On the MAP/G/1 queue with Lebesgue-dominated service time distribution and LCFS preemptive repeat service discipline

Stochastic Models

Volumn 18, Issue 4, 2002, Pages 589-595

  Breuer, Lothar ^a  

^a UNIVERSITY OF TRIER   (Germany)

Author keywords

Last come first served; MAP; Preemptive repeat; QBD

Indexed keywords

ASYMPTOTIC STABILITY; MARKOV PROCESSES; MATHEMATICAL MODELS; MAXIMUM PRINCIPLE; PROBABILITY DISTRIBUTIONS; RECURSIVE FUNCTIONS; THEOREM PROVING; TIME SERIES ANALYSIS;

LAST COM FIRST SERVED DISTRIBUTION; LEBESGUE SERVICE TIME DISTRIBUTION; MARKOV RENEWAL THEORY; MAXIMUM A POSTERIORI QUEUE; RECURSIVE FORMULA; STATIONARY DISTRIBUTION; TRANSIENT DISTRIBUTION;

QUEUEING THEORY;

EID: 0036966546     PISSN: 15326349     EISSN: None     Source Type: Journal    
DOI: 10.1081/STM-120016446     Document Type: Article

References (20)

1. He, Q.-M.; Alfa, A.S. The MMAP[K]/PH[K]/1 Queues with a Last-Come-First-Served Preemptive Service Discipline. Queueing Syst. 1998, 29 (2-4), 269-291.
2. Gaur, K.N. Preemptive Repeat-Different Priority Queue. Pure Appl. Math. Sci. 1976, 3, 73-80.
3. Gaur, K.N. Time-Independent Solution of the Preemptive-Repeat Priority Queue with Bulk Arrivals. Pure Appl. Math. Sci. 1979, 9, 43-51.
4. Kumar, V.; Singh, T.P.; Iqbal, M. k-Phase Service Mechanism Under Pre-emptive Priority Service Rule. Pure Appl. Math. Sci. 1983, 17, 41-48.
5. Miyazawa, M. On the System Queue Length Distributions of LCFS-P Queues with Arbitrary Acceptance and Restarting Policies. J. Appl. Probab. 1992, 29 (2), 430-440.
6. Pechinkin, A.V. Service Characteristics in the System GI/GI/1/∞ with a Last Come, First Serve Preemptive Repeat Priority Discipline. Autom. Remote Control 1993, 54, 978-988.
7. Machihara, F. A Preemptive Priority Queue as a Model with Server Vacations. J. Oper. Res. Soc. Jpn 1996, 39 (1), 118-131.
8. Machihara, F. A Preemptive Priority Queue with Nonrenewal Inputs. In Matrix-Analytic Methods in Stochastic Models; Chakravarthy, S.R., Alfa, A.S., Eds.; Marcel Dekker: New York, NY, 1997; 21-42.
9. He, Q.-M.; Alfa, A.S. Computational Analysis of MMAP[K]/PH[K]/1 Queues with a Mixed FCFS and LCFS Service Discipline. Nav. Res. Logist. 2000, 47 (5), 399-421.
10. He, Q.-M.; Alfa, A.S. The Discrete Time MMAP[K]/PH[K]/1/LCFS-GPR Queue and Its Variants. In Advances in Algorithmic Methods for Stochastic Models; Latouche, G., Taylor, P., Eds.; Notable Publications: New Jersey, USA, 2000; 167-190.
11. Davis, M.H.A. Markov Models and Optimization; Chapman & Hall: London, 1993.
12. Neuts, M.F. A Versatile Markovian Point Process. J. Appl. Probab. 1979, 16, 764-774.
13. Lucantoni, D.M. New Results on the Single Server Queue with a Batch Markovian Arrival Process. Commun. Stat., Stoch. Models 1991, 7 (1), 1-46.
14. Asmussen, S.; Koole, G. Marked Point Processes as Limits of Markovian Arrival Streams. J. Appl. Probab. 1993, 30 (2), 365-372.
15. Breuer, L. On Markov-Additive Jump Processes. Queueing Syst. 2002, 40 (1), 75-91.
16. Breuer, L. An EM Algorithm for Batch Markovian Arrival Processes and Its Comparison to a Simpler Estimation Procedure. Ann. Oper. Res. 2002, 112, in press.
17. Çinlar, E. Introduction to Stochastic Processes; Prentice-Hall: Englewood Cliffs, NJ, 1975.
18. Bellman, R. Introduction to Matrix Analysis; SIAM: Philadelphia, PA, 1997.
19. Latouche, G.; Ramaswami, V. A Logarithmic Reduction Algorithm for Quasi-birth-Death Processes. J. Appl. Probab. 1993, 30 (3), 650-674.
20. Latouche, G.; Ramaswami, V. Introduction to Matrix Analytic Methods in Stochastic Modeling; SIAM: Philadelphia, PA, 1999.