The processor-sharing queue with bulk arrivals and phase-type services

Performance Evaluation

Volumn 64, Issue 4, 2007, Pages 277-297

  Kim, Jeongsim ^a   Kim, Bara ^b  

^a Chungbuk National University   (South Korea)

^b Korea University   (South Korea)

Author keywords

Bulk arrivals; Joint transform; Processor sharing; Queue length; Sojourn time

Indexed keywords

LINEAR EQUATIONS; MATHEMATICAL TRANSFORMATIONS; PROGRAM PROCESSORS; QUEUEING THEORY;

BULK ARRIVALS; JOINT TRANSFORM; PROCESSOR-SHARING; QUEUE-LENGTH; SOJOURN TIME;

POISSON DISTRIBUTION;

EID: 33846271059     PISSN: 01665316     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.peva.2006.05.006     Document Type: Article

References (21)

1. Asare B.K., and Foster F.G. Conditional response time in the M / G / 1 processor-sharing system. J. Appl. Probab. 20 (1983) 910-915
2. Avrachenkov K., Ayesta U., and Brown P. Batch arrival processor-sharing queue with application to multilevel processor-sharing scheduling. Queueing Syst. 50 (2005) 459-480
3. Bansal N. Analysis of the M / G / 1 processor-sharing queue with bulk arrivals. Oper. Res. Lett. 31 (2003) 401-405
4. Bickley W.G., and McNamee J. Matrix and other direct methods for the solution of systems of linear difference equations. Philos. Trans. R. Soc. Lond. Ser. A 252 (1960) 69-131
5. Bartels R.H., and Stewart G.W. Solution of the matrix equation AX + XB = C. Comm. ACM 15 (1972) 820-826
6. Coffman Jr. E.G., Muntz R.R., and Trotter H. Waiting time distribution for processor-sharing systems. J. ACM 17 (1970) 123-130
7. X / G / 1 processor sharing queues, Tech. Rep., CUCS-006-04, Columbia University, 2003
8. Grishechkin S. G I / G / 1 processor sharing queue in heavy traffic. Adv. in Appl. Probab. 26 (1994) 539-555
9. Jagerman D.L., and Sengupta B. The G I / M / 1 processor-sharing queue and its heavy-traffic analysis. Stoch. Models 7 (1991) 379-396
10. Kim J., and Kim B. Sojourn time distribution in the M / M / 1 queue with discriminatory processor-sharing. Perform. Eval. 58 (2004) 341-365
11. Kleinrock L. Time-shared systems: A theoretical treatment. J. ACM 14 (1967) 242-261
12. Kleinrock L., Muntz R.R., and Rodemich E. The processor-sharing queueing model for time-shared systems with bulk arrivals. Networks 1 (1971) 1-13
13. Knessl C. Asymptotic approximation for the G I / M / 1 queue with processor-sharing service. Stoch. Models 8 (1992) 1-34
14. Masuyama H., and Takine T. Sojourn time distribution in M A P / M / 1 processor-sharing queue. Oper. Res. Lett. 31 (2003) 406-412
15. Ott T.J. The sojourn time distribution in the M / G / 1 queue with processor sharing. J. Appl. Probab. 21 (1984) 360-378
16. Ramaswami V. The sojourn time in the G I / M / 1 queue with processor sharing. J. Appl. Probab. 21 (1984) 445-450
17. Rege K.M., and Sengupta B. The M / G / 1 processor-sharing queue with bulk arrivals. Modelling and Performance Evaluation of ATM Technology (1993), Elsevier, Amsterdam 417-432
18. Schassberger R. A new approach to the M / G / 1 processor-sharing queue. Adv. Appl. Probab. 16 (1984) 202-213
19. Seneta E. Non-negative Matrices and Markov Chains. 2nd edition (1981), Springer-Verlag, New York
20. Sengupta B. An approximation for the sojourn-time distribution for the G I / G / 1 processor-sharing queue. Stoch. Models 8 (1992) 35-57
21. Yashkov S.F. Processor-sharing queues: Some progress in analysis. Queueing Syst. 2 (1987) 1-17