Embedded renewal processes in the GI/G/s queue

The stable GI/G/s queue (ρ GI/G /1 queue, but a simple GI/G /2 example is given here with all interarrival time and service time moments finite and ρ GI/G /1 and GI/G/s queues are discussed. For example, functional limit theorems for time-average or cumulative processes associated with a large class of GI/G/s queues in light traffic are implied.

[1]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

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

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

[4]  D. V. Lindley,et al.  The theory of queues with a single server , 1952, Mathematical Proceedings of the Cambridge Philosophical Society.

[5]  D. Blackwell.  Extension of a renewal theorem , 1953 .

[6]  Walter L. Smith.  On the distribution of queueing times , 1953, Mathematical Proceedings of the Cambridge Philosophical Society.

[7]  Walter L. Smith,et al.  Regenerative stochastic processes , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  J. Kiefer,et al.  On the theory of queues with many servers , 1955 .

[9]  J. Wolfowitz,et al.  On the Characteristics of the General Queueing Process, with Applications to Random Walk , 1956 .

[10]  Walter L. Smith.  Renewal Theory and its Ramifications , 1958 .

[11]  P. D. Finch.  On the distribution of queue size in queueing problems , 1959 .

[12]  R. M. Loynes,et al.  Stationary Waiting-Time Distributions for Single-Server Queues , 1962 .

[13]  R. M. Loynes,et al.  The stability of a queue with non-independent inter-arrival and service times , 1962, Mathematical Proceedings of the Cambridge Philosophical Society.

[14]  L. Takács.  THE LIMITING DISTRIBUTION OF THE VIRTUAL WAITING TIME AND THE QUEUE SIZE FOR A SINGLE-SERVER QUEUE WITH RECURRENT INPUT AND GENERAL SERVICE TIMES , 1963 .

[15]  C. C. Heyde.  Two Probability Theorems and Their Application to Some First Passage Problems , 1964 .

[16]  J. Kingman.  On the algebra of queues , 1966, Journal of Applied Probability.

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

[18]  IDENTIFIABILITY IN GI/G/K QUEUES , 1970 .

[19]  J.H.A. De Smit,et al.  Many server queieing systems , 1971 .

[20]  D. Iglehart.  Functional limit theorems for the queue GI/G/1 in light traffic , 1971, Advances in Applied Probability.

[21]  Richard F. Serfozo,et al.  Semi-stationary processes , 1972 .

[22]  D. Iglehart.  Extreme Values in the GI/G/1 Queue , 1972 .

[23]  S. Stidham.  Regenerative processes in the theory of queues, with applications to the alternating-priority queue , 1972, Advances in Applied Probability.

[24]  S. Ross,et al.  ASYMPTOTIC PROPERTIES OF CUMULATIVE PROCESSES , 1972 .