Performance Analysis of Retrial Queueing Systems Using Generalized Stochastic Petri Nets

Abstract We consider retrial queueing systems, in which an arriving customer finding the server busy, may repeat his call after a random duration. The consideration of repeated calls introduces great analytical difficulties. In fact, detailed analytical results exist for some special retrial queueing systems, while for many others, the performance evaluation is limited to numerical algorithms, approximation methods and simulation. Retrial queues have been widely used to model many problems in telephone switching systems, telecommunication and computer networks. In this paper, we show a method of modelling and analysing retrial queueing systems, using the Generalized Stochastic Petri nets (GSPNs).

[1]  Kishor S. Trivedi,et al.  Recent Developments in Non-Markovian Stochastic Petri Nets , 1998, J. Circuits Syst. Comput..

[2]  Reinhard German,et al.  Analysis of Stochastic Petri Nets by the Method of Supplementary Variables , 1994, Perform. Evaluation.

[3]  Marco Ajmone Marsan,et al.  Modelling with Generalized Stochastic Petri Nets , 1995, PERV.

[4]  Bara Kim,et al.  MAP1, MAP2/M/c retrial queue with guard channels and its application to cellular networks , 1999 .

[5]  Jewgeni H. Dshalalow,et al.  Frontiers in Queueing: Models and Applications in Science and Engineering , 1997 .

[6]  Shang Zhi,et al.  A proof of the queueing formula: L=λW , 2001 .

[7]  Marco Ajmone Marsan,et al.  Generalized Stochastic Petri Nets: A Definition at the Net Level and Its Implications , 1993, IEEE Trans. Software Eng..

[8]  Michael K. Molloy.  Performance Analysis Using Stochastic Petri Nets , 1982, IEEE Transactions on Computers.

[9]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[10]  T. T. Soong,et al.  Book Reviews : INTRODUCTION TO STOCHASTIC PROCESSES E. Cinlar Prentice-Hall, 1975 , 1979 .

[11]  J. George Shanthikumar,et al.  Design of manufacturing systems using queueing models , 1992, Queueing Syst. Theory Appl..

[12]  Gennadi Falin,et al.  A survey of retrial queues , 1990, Queueing Syst. Theory Appl..

[13]  J. Little.  A Proof for the Queuing Formula: L = λW , 1961 .

[14]  R. I. Wilkinson.  Theories for toll traffic engineering in the U. S. A. , 1956 .

[15]  Hui Li,et al.  An approximation method for the M/G/1 retrial queue with general retrial times , 1994 .

[16]  Bong Dae Choi,et al.  Single server retrial queues with priority calls , 1999 .

[17]  Jesús R. Artalejo,et al.  Accessible bibliography on retrial queues , 1999 .

[18]  Gianni Conte,et al.  Analysis of large GSPN models: a distributed solution tool , 1997, Proceedings of the Seventh International Workshop on Petri Nets and Performance Models.

[19]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[20]  Vidyadhar G. Kulkarni,et al.  Retrial queues revisited , 1998 .

[21]  J. Templeton.  Retrial queues , 1999 .

[22]  Giovanni Chiola,et al.  GreatSPN 1.7: Graphical Editor and Analyzer for Timed and Stochastic Petri Nets , 1995, Perform. Evaluation.

[23]  Kishor S. Trivedi,et al.  Markov regenerative models , 1995, Proceedings of 1995 IEEE International Computer Performance and Dependability Symposium.

[24]  Kishor S. Trivedi,et al.  SPNP: stochastic Petri net package , 1989, Proceedings of the Third International Workshop on Petri Nets and Performance Models, PNPM89.

[25]  Jesus R. Artalejo,et al.  Analysis of an M/G/1 queue with constant repeated attempts and server vacations , 1997, Comput. Oper. Res..

[26]  Marcel F. Neuts,et al.  Numerical investigation of a multiserver retrial model , 1990, Queueing Syst. Theory Appl..

[27]  Tao Yang,et al.  A single-server retrial queue with server vacations and a finite number of input sources , 1995 .