Imbedding equations in queueing theory

Recursive equations in finite Markov chain imbedding

Abstract In this paper, recursive equations for waiting time distributions of r-th occurrence of a compound pattern are studied via the finite Markov chain imbedding technique under overlapping and non-overlapping counting schemes in sequences of independent and identically distributed (i.i.d.) or Markov dependent multi-state trials. Using the relationship between number of patterns and r-th wa...

Queueing Theory

Queueing Theory

A queue is a waiting line (like customers waiting at a supermarket checkout counter); queueing theory is the mathematical theory of waiting lines. More generally, queueing theory is concerned with the mathematical modeling and analysis of systems that provide service to random demands. A queueing model is an abstract description of such a system. Typically, a queueing model represents (1) the s...

Invariant Imbedding and the Integration of Hamilton's Equations

Queueing Theory with Reneging

The literature on queueing with reneging is reviewed. Only random (Poisson) arrivals and unlimited capacity queues are considered, although some of the references also contain results for other arrival distributions or finite capacity queues. The paper focuses on the probability of service under steady state conditions; results for other metrics such as the expected waiting time may be found in...