A single server queue with mixed types of interruptions : application to the modelling of checkpointing and recovery in a transactional system

SummaryThe 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.

[1]  F. V..  Markovian Models of a Transactronal System Supported by Checkpointing and Recovery Strategies. Part 2: a Model with a Specifiect Number of Completed Transactions between Checkpoints , 2002 .

[2]  W Versnel.  The circular hall plate : approximation of the geometrical correction factor for small contacts , 1981 .

[3]  Terry Williams,et al.  Probability and Statistics with Reliability, Queueing and Computer Science Applications , 1983 .

[4]  Erol Gelenbe,et al.  Performance of rollback recovery systems under intermittent failures , 1978, CACM.

[5]  Ward Whitt,et al.  On Arrivals That See Time Averages , 1990, Oper. Res..

[6]  A. P. Verlijsdonk.  On the application of biphase coding in data communication systems , 1982 .

[7]  François Baccelli.  Analysis of a service facility with periodic checkpointing , 2004, Acta Informatica.

[8]  S K Trivedi,et al.  A Unified Model for the Analysis of Job Completion Time and Performability Measures in Fault-Tolerant Systems , 1985 .

[9]  D. Gaver.  A Waiting Line with Interrupted Service, Including Priorities , 1962 .

[10]  Victor F. Nicola,et al.  A Markovian Model, with State-Dependent Parameters, of a Transactional System Supported by Checkpointing and Recovery Strategies , 1983, MMB.

[11]  W. Versnel,et al.  Fabrication of planar semiconductor diodes : an educational laboratory experiment , 1981 .

[12]  Robert M. Oliver.  AN ALTERNATE DERIVATION OF THE POLLACZEK KHINTCHINE FORMULA , 1963 .

[13]  Kishor S. Trivedi.  Probability and Statistics with Reliability, Queuing, and Computer Science Applications , 1984 .

[14]  Victor F. Nicola,et al.  A Model of Checkpointing and Recovery with a Specified Number of Transactions between Checkpoints , 1983, Performance.

[15]  Linda Green,et al.  Technical Note - A Limit Theorem on Subintervals of Interrenewal Times , 1982, Oper. Res..

[16]  K Fabian.  Design and implementation of a central instruction processor with a multimaster bus interface , 1981 .

[17]  Aah Ad Damen,et al.  The page matrix : an excellent tool for noise filtering of Markov parameters, order testing and realization , 1982 .

[18]  Erol Gelenbe,et al.  Analysis and Synthesis of Computer Systems , 1980 .

[19]  Erol Gelenbe,et al.  On the Optimum Checkpoint Interval , 1979, JACM.

[20]  Andrzej Duda,et al.  Performance Analysis of the Checkpoint-Rollback-Recovery System via Diffusion Approximation , 1983, Computer Performance and Reliability.

[21]  N. K. Jaiswal,et al.  Priority queues , 1968 .

[22]  Wjm Pim Lemmens.  The PAP preprocessor : a precompiler for a language for concurrent processing on a multiprocessor system , 1982 .

[23]  Vf Nicola.  Markovian models of a transactional system supported by checkpointing and recovery strategies, Part 1: A model with state-dependent parameters , 1982 .

[24]  Ronald W. Wolff,et al.  Poisson Arrivals See Time Averages , 1982, Oper. Res..

[25]  A Krolikowski,et al.  Model structure selection in linear system identification : survey of methods with emphasis on the information theory approach , 1982 .

[26]  Mf Ponomarenko,et al.  Information measures and their applications to identification : a bibliography , 1981 .

[27]  S K Trivedi,et al.  On Modeling the Performance and Reliability of Multi-Mode Computer Systems , 1984 .