An introduction to difference equations
An introduction to difference equations
On the M/M/1 Queue with Catastrophes and Its Continuous Approximation
Queueing Systems: Theory and Applications
Stochastic Decomposition in M/M/∞ Queues with Markov Modulated Service Rates
Queueing Systems: Theory and Applications
Analysis of customers' impatience in queues with server vacations
Queueing Systems: Theory and Applications
Queues with system disasters and impatient customers when system is down
Queueing Systems: Theory and Applications
Infinite-server queues with system's additional tasks and impatient customers
Probability in the Engineering and Informational Sciences
q-series in markov chains with binomial transitions: Studying a queue with synchronization
Probability in the Engineering and Informational Sciences
Synchronized reneging in queueing systems with vacations
Queueing Systems: Theory and Applications
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In this paper we present a detailed analysis of a single server Markovian queue with impatient customers. Instead of the standard assumption that customers perform independent abandonments, we consider situations where customers abandon the system simultaneously. Moreover, we distinguish two abandonment scenarios; in the first one all present customers become impatient and perform synchronized abandonments, while in the second scenario we exclude the customer in service from the abandonment procedure. Furthermore, we extend our analysis to the M/M/c queue under the second abandonment scenario.For these models we carry out an extensive analysis including the stationary, the busy period and the conditional sojourn time distributions deriving exact formulas and iterative algorithmic schemes. We also obtain explicit results under various limiting regimes that demonstrate the effect of the level of synchronization on the performance of the systems.