Sojourn Time Distribution of the Asymmetric M/M/1//N-System with LCFS-PR Service

In this paper we present a recursive deenition of the sojourn time probability distribution function of the M= M=1==N{LCFS-PR system. Applications of this model can befound in telecommunication systems and in manufacturing systems. By means of a transformation method we obtain the rst two moments of sojourn times in a symmetric system with an arbitrary number of messages. This result is generalized regarding heterogeneous messages with diierent service requirementss yet it is applied to only two messages. Finally we n umerically compare the variance of sojourn times to the FCFS case for which we derive an explicit expression.

[1]  David R. Cox,et al.  The Productivity of Machines Requiring Attention at Random Intervals , 1951 .

[2]  R. R. P. Jackson,et al.  Introduction to the Theory of Queues , 1963 .

[3]  L. Durr.  A Single-Server Priority Queuing System with General Holding Times, Poisson Input, and Reverse-Order-of-Arrival Queuing Discipline , 1969, Oper. Res..

[4]  John W. Boyse,et al.  A Straightforward Model for Computer Performance Prediction , 1975, CSUR.

[5]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[6]  Hisashi Kobayashi,et al.  Modeling and analysis , 1978 .

[7]  Stephen S. Lavenberg,et al.  Mean-Value Analysis of Closed Multichain Queuing Networks , 1980, JACM.

[8]  P. Moran,et al.  Reversibility and Stochastic Networks , 1980 .

[9]  K. Mani Chandy,et al.  Computer Systems Performance Modeling , 1981 .

[10]  H. Martz.  Bayesian reliability analysis , 1982 .

[11]  Daniel P. Heyman.  Stochastic models in operations research, volume I : stochastic processes and operating characteristics / Daniel P. Heyman, Matthew J. Sobel , 1982 .

[12]  K. Mani Chandy,et al.  A Characterization of Product-Form Queuing Networks , 1983, JACM.

[13]  Kathryn E. Stecke,et al.  REVIEW OF OPERATOR/MACHINE INTERFERENCE MODELS. , 1985 .

[14]  Eric Allender,et al.  A note on the power of threshold circuits , 1989, 30th Annual Symposium on Foundations of Computer Science.

[15]  Lane A. Hemaspaandra,et al.  Using Inductive Counting to Simulate Nondeterministic Computation , 1990, MFCS.

[16]  Ulrich Hertrampf,et al.  Relations Among Mod-Classes , 1990, Theor. Comput. Sci..

[17]  Klaus W. Wagner,et al.  Bounded Query Classes , 1990, SIAM J. Comput..

[18]  Miroslaw Kowaluk,et al.  Vector Language: Simple Description of Hard Instances (Extended Abstract) , 1990, MFCS.

[19]  Eric Allender,et al.  On the Power of Uniform Families of Constant Depth Treshold Circuits , 1990, MFCS.

[20]  Conny Friedewald,et al.  WUMPS, Würzburger Message Passing System , 1990, Transputer-Anwender-Treffen.

[21]  Phuoc Tran-Gia,et al.  Approximate Performance Analysis of the DQDB Acess Protocol , 1990, Comput. Networks ISDN Syst..

[22]  P. Tran-Gia,et al.  A discrete time analysis of the DQDB access protocol with general input traffic , 1990, SBT/IEEE International Symposium on Telecommunications.

[23]  Hermann Gold,et al.  Multi Server Batch Service Systems in Push and Pull Operating Mode - a Performance Comparison , 1991 .

[24]  Phuoc Tran-Gia,et al.  Performance analysis of the CRMA-protocol in high-speed networks , 1991, Performance of Distributed Systems and Integrated Communication Networks.

[25]  Phuoc Tran-Gia,et al.  A layered description of ATM cell traffic streams and correlation analysis , 1991, IEEE INFCOM '91. The conference on Computer Communications. Tenth Annual Joint Comference of the IEEE Computer and Communications Societies Proceedings.

[26]  F Hh,et al.  Queueing Analysis of Resource Dispatching and Scheduling in Multi-media Systems , 1991 .

[27]  Christoph Meinel,et al.  Structure and Importance of Logspace-MOD-Classes , 1991, STACS.

[28]  F Hh,et al.  Discrete-time Analysis of the Output Process of an Atm Multiplexer with Periodic Input , 1991 .

[29]  T. Fritsch,et al.  Communication network routing using neural nets-numerical aspects and alternative approaches , 1991, [Proceedings] 1991 IEEE International Joint Conference on Neural Networks.

[30]  M. Ritter,et al.  Blocking in Multi-service Broadband Systems with Cbr and Vbr Input Traac , 1992 .

[31]  Frank Puppe,et al.  COKE: efficient solving of complex assignment problems with the propose-and-exchange method , 1992, Proceedings Fourth International Conference on Tools with Artificial Intelligence TAI '92.

[32]  Jack H. Lutz,et al.  On Complexity Classes and Algorithmically Random Languages (Extended Abstract) , 1992, STACS.

[33]  Phuoc Tran-Gia,et al.  An Analysis of Multi-Service Systems with Trunk Reservation Mechanisms , 1992 .

[34]  F Hh.  Autocorrelation and Power Density Spectrum of Atm Multiplexer Output Processes , 1992 .

[35]  Manfred Mittler,et al.  Triggering Scheduler , 1993 .

[36]  Phuoc Tran-Gia,et al.  Performance analysis of a batch service queue arising out of manufacturing system modelling , 1993, Queueing Syst. Theory Appl..

[37]  Heribert Vollmer,et al.  The Complexity of Finding Middle Elements , 1993, Int. J. Found. Comput. Sci..

[38]  Phuoc Tran-Gia,et al.  Basic Concepts and Performance of High-Speed Protocols , 1993, Integrated Broadband Communications.

[39]  R. Dittmann,et al.  Discrete-time Analysis of a Cyclic Service System with Gated Limited Service , 1993 .

[40]  N Gerlich,et al.  Reducing the Variance of Sojourn times in Queueing Networks with Overtaking , 1993 .

[41]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[42]  Phuoc Tran-Gia,et al.  Performance of a neural net scheduler used in packet switching interconnection networks , 1993, IEEE International Conference on Neural Networks.

[43]  Krzysztof Lorys,et al.  The Variable Membership Problem: Succinctness Versus Complexity , 1994, STACS.

[44]  Phuoc Tran-Gia,et al.  Structure and Performance of Neural Nets in Broadband System Admission Control , 1994 .

[45]  M. R. Fraterz,et al.  Delivery of Mpeg Video Services over Atm , 1994 .

[46]  M. Ritter.  Analysis of the Generic Cell Rate Algorithm Monitoring ON/OFF-Traffic , 1994 .

[47]  U Rothaugy,et al.  Artiicial Neural Networks Used for Way Optimization in Multi-head Systems in Application to Electrical Flying Probe Testers , 1994 .

[48]  F. H. Ubner,et al.  Performance Analysis of Source Policing Architectures in ATM Systems , 1994 .

[49]  Hermann Gold,et al.  Performance Analysis of a Batch Service System , 1994 .

[50]  Michael R. Frater,et al.  A Comparison of Models for VBR Video Traffic Sources in B-ISDN , 1994, Broadband Communications.

[51]  Phuoc Tran-Gia,et al.  Discrete-time analysis of cell spacing in ATM systems , 1994, Telecommun. Syst..

[52]  F Hh,et al.  Output Process Analysis of the Peak Cell Rate Monitor Algorithm , 1994 .

[53]  Reiner Kolla,et al.  Optimal technology mapping for single output cells , 1995, Proceedings. Fifth Great Lakes Symposium on VLSI.

[54]  Heribert Vollmer,et al.  Recursion Theoretic Characterizations of Complexity Classes of Counting Functions , 1996, Theor. Comput. Sci..

[55]  Heribert Vollmer,et al.  Classes of Counting Functions and Complexity Theoretic Operators , 1996 .