The single server M/G/1 queue subject to Poisson interruptions has many useful applications in computer systems modeling. The interruptions are usually characterized by their type of service-preemption discipline. This paper deals with this model in its most general setting, allowing the simultaneous presence of all types of interruptions that may be encountered in real systems. Inspite of the inherent complexity of the analysis, it is possible to derive analytic closed form expressions for interesting performance measures. The results obtained are of theoretical interest as well as of practical significance. In particular, we derive the Laplace Stieltjes transform of the completion time associated with a customer's Śervice and obtain the steady-state average number of customers in the system. An application to the modeling of checkpointing and recovery in a transactional system is considered.
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Baccelli, F.: Analysis of a Service Facility with Periodic Checkpointing. Acta Inf. 15, 67–81 (1981)
Baccelli, F., Znati, T.: Queueing Algorithms with Breakdowns in Database Modeling. F.J. Kylstra, ed., pp. 213–231. Amsterdam: North Holland 1981
Duda, A.: Performance Analysis of the Checkpoint-Rollback-Recovery System via Diffusion Approximation. In: Proc. Int. Workshop on Applied Mathematics and Performance/Reliability Models of Computer/Communication Systems. G. Iazeolla and S. Tucci, eds., pp. 387–399. Amsterdam: North Holland 1983
Gaver, D.P.: A Waiting Line with Interrupted Service, Including Priorities. J. R. Stat. Soc., Ser. B 24, 73–90 (1962)
Gelenbe, E., Derochette, D.: Performance of Rollback Recovery Systems Under Intermittent Failures. Commun. ACM 21, 493–499 (1978)
Gelenbe, E.: On the Optimum Checkpoint Interval. J. ACM 26, 259–270 (1979)
Gelenbe, E., Mitrani, I.: Analysis and Synthesis of Computer Systems. New York: Academic Press 1980
Green, L.: A Limit Theorem on Subintervals of Interrenewal Times. Oper. Res. 30, 210–216 (1982)
Jaiswal, N.K.: Priority Queues. New York: Academic Press 1968
Kulkarni, V.G., Nicola, V.F., Trivedi, K.S.: On Modeling the Performance and Reliability of Multi-Mode Computer Systems. (To appear, in J. Syst. Software)
Kulkarni, V.G., Nicola, V.F., Trivedi, K.S., Smith, R.M.: A Unified Model for the Analysis of Job Completion Time and Performability Measures in Fault-Tolerant Systems. Technical Report, CS-1985-13 Dept. of Computer Science, Duke University, 1985
Nicola, V.F., Kylstra, F.J.: A Markovian Model, with State-Dependent Parameters, of a Transactional System Supported by Checkpointing and Recovery Strategies. In: Messung, Modellierung und Bewertung von Rechensystemen, IFB61. P.J. Kuhn and K.M. Schulz, eds., pp. 189–206. Heidelberg, Berlin, New York: Springer 1983
Nicola, V.F., Kylstra, F.J.: A Model of Checkpointing and Recovery with a Specified Number of Transactions Between Checkpoints. A.K. Agrawala and S.K. Tripathi, eds., pp. 83–100. Amsterdam: North Holland 1983
Oliver, R.M.: An Alternate Derivation of the Pollaczek-Khintchine Formula. Oper. Res. 12, 158–159 (1964)
Trivedi, K.S.: Probability and Statistics with Reliability, Queueing and Computer Science Applications. Englewood Cliffs, N.J.: Prentice Hall 1982
Wolff, R.W.: Poisson Arrivals See Time Averages. Oper. Res. 30, 223–231 (1982)
This work was supported in part by Air Force Office of Scientific Research under grant AFOSR-84-0132, by the Army Research Office under contract DAAG29-84-K0045 and by the National Science Foundation under grant MCS-830200
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Nicola, V.F. A single server queue with mixed types of interruptions. Acta Informatica 23, 465–486 (1986). https://doi.org/10.1007/BF00267867
- Computer System
- Completion Time
- Real System
- Mixed Type
- Closed Form Expression