Queues with Server Vacations and Levy Processes with Secondary Jump Input

byOffer Kella* and Ward Whitt**November 16, 1989Revision: June 5, 1990American Mathematical Society 1980 subject classifications. Primary 60J30; secondary 60K25,60K30.Key words and phrases. Le ´ vy processes, queueing theory, queues with server vacations, queueswith service interruptions, stochastic decomposition, martingales, M/G/1 queue, Pollaczek-Khinchine formula.* Department of Operations Research, Yale University, 84 Trumbull Street, New Haven, CT06520** AT&T Bell Laboratories, Room 2C-178, 600 Mountain Avenue, Murray Hill, NJ 07974-2070.

[1]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[2]  N. U. Prabhu,et al.  Stochastic Storage Processes , 1980 .

[3]  B. T. Doshi,et al.  Queueing systems with vacations — A survey , 1986, Queueing Syst. Theory Appl..

[4]  J. George Shanthikumar.  Level crossing analysis of priority queues and a conservation identity for vacation models , 1989 .

[5]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[6]  Robert B. Cooper.  Queues served in cyclic order: Waiting times , 1970, Bell Syst. Tech. J..

[7]  J. George Shanthikumar.  On Stochastic Decomposition in M/G/1 Type Queues with Generalized Server Vacations , 1988, Oper. Res..

[8]  U. Yechiali,et al.  Utilization of idle time in an M/G/1 queueing system Management Science 22 , 1975 .

[9]  Feller William,et al.  An Introduction To Probability Theory And Its Applications , 1950 .

[10]  J. Michael Harrison.  The supremum distribution of a Lévy process with no negative jumps , 1977, Advances in Applied Probability.

[11]  Kai Lai Chung,et al.  A Course in Probability Theory , 1949 .

[12]  Walter A. Rosenkrantz.  Calculation of the Laplace Transform of the Length of the Busy Period for the M|G|1 Queue Via Martingales , 1983 .

[13]  J. Harrison,et al.  Brownian motion and stochastic flow systems , 1986 .

[14]  Ward Whitt,et al.  Ordinary CLT and WLLN Versions of L = λW , 1988, Math. Oper. Res..

[15]  N. H. Bingham,et al.  Fluctuation theory in continuous time , 1975, Advances in Applied Probability.

[16]  Jacques Teghem,et al.  Control of the service process in a queueing system , 1986 .

[17]  Armand M. Makowski,et al.  Dynamic, Transient and Stationary Behavior of the M/GI/1 Queue. , 1989 .

[18]  P. Brémaud.  Point Processes and Queues , 1981 .

[19]  Robert B. Cooper,et al.  Stochastic Decompositions in the M/G/1 Queue with Generalized Vacations , 1985, Oper. Res..

[20]  Bharat T. Doshi.  Conditional and unconditional distributions forM/G/1 type queues with server vacations , 1990, Queueing Syst. Theory Appl..

[21]  W. Whitt,et al.  Diffusion approximations for queues with server vacations , 1990, Advances in Applied Probability.

[22]  V. Zolotarev.  The First Passage Time of a Level and the Behavior at Infinity for a Class of Processes with Independent Increments , 1964 .