Queueing Systems: Theory and Applications - Special issue of queueing systems, theory and applications
Stability Conditions for Some Typical Retrial Queues
Cybernetics and Systems Analysis
Analysis of customers' impatience in queues with server vacations
Queueing Systems: Theory and Applications
A multiserver retrial queue: regenerative stability analysis
Queueing Systems: Theory and Applications
Stationary delays for a two-class priority queue with impatient customers
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Synchronized reneging in queueing systems with vacations
Queueing Systems: Theory and Applications
An M/G/1 retrial G-queue with non-exhaustive random vacations and an unreliable server
Computers & Mathematics with Applications
Stability of Markov modulated discrete-time dynamic systems
Automatica (Journal of IFAC)
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We consider the following type of problems. Calls arrive at a queue of capacity K (which is called the primary queue), and attempt to get served by a single server. If upon arrival, the queue is full and the server is busy, the new arriving call moves into an infinite capacity orbit, from which it makes new attempts to reach the primary queue, until it finds it non-full (or it finds the server idle). If the queue is not full upon arrival, then the call (customer) waits in line, and will be served according to the FIFO order. If \lambda is the arrival rate (average number per time unit) of calls and \mu is one over the expected service time in the facility, it is well known that \mu\lambda is not always sufficient for stability. The aim of this paper is to provide general conditions under which it is a sufficient condition. In particular, (i) we derive conditions for Harris ergodicity and obtain bounds for the rate of convergence to the steady state and large deviations results, in the case that the inter-arrival times, retrial times and service times are independent i.i.d. sequences and the retrial times are exponentially distributed; (ii) we establish conditions for strong coupling convergence to a stationary regime when either service times are general stationary ergodic (no independence assumption), and inter-arrival and retrial times are i.i.d. exponentially distributed; or when inter-arrival times are general stationary ergodic, and service and retrial times are i.i.d. exponentially distributed; (iii) we obtain conditions for the existence of uniform exponential bounds of the queue length process under some rather broad conditions on the retrial process. We finally present conditions for boundedness in distribution for the case of nonpatient (or non persistent) customers.