A single-server batch arrival queue with returning customers

We consider a new class of batch arrival retrial queues. By contrast to standard batch arrival retrial queues we assume if a batch of primary customers arrives into the system and the server is free then one of the customers starts to be served and the others join the queue and then are served according to some discipline. With the help of Lyapunov functions we have obtained a necessary and sufficient condition for ergodicity of embedded Markov chain and the joint distribution of the number of customers in the queue and the number of customers in the orbit in steady state. We also have suggested an approximate method of analysis based on the corresponding model with losses.Queueing Markov processes Retrials Batch arrivals Steady state

Stochastic decomposition for retrial queues

retrial queues, stochastic decomposition property, vacation models, factorial cumulants, rate of convergence,

AnM/M/c queue with impatient customers

M/M/c Queue, Impatient Customers, Loss Probability, 60K25, 68M20,

BMAP|SM⥻1 model with Markov modulated retrials

Batch Markovian Arrival Process, Semi-Markovian Service, Markov Modulated Retrial Poisson Process, 60K25,

A retrial model in a nonstationary regime

Retrial Queueing Systems, Renewal Markovian Process, Semiregenerative Process,