On arrivals that see time averages
Operations Research
On the M(n)/M(n)/s queue with impatient calls
Performance Evaluation
IEEE Transactions on Computers
On queueing with customer impatience until the beginning of service
Queueing Systems: Theory and Applications
Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System
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
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Consider a number of parallel queues, each with an arbitrary capacity and multiple identical exponential servers. The service discipline in each queue is first-come-first-served (FCFS). Customers arrive according to a state-dependent Poisson process. Upon arrival, a customer joins a queue according to a state-dependent policy or leaves the system immediately if it is full. No jockeying among queues is allowed. An incoming customer to a parallel queue has a general patience time dependent on that queue after which he/she must depart from the system immediately. Parallel queues are of two types: type 1, wherein the impatience mechanism acts on the waiting time; or type 2, a single server queue wherein the impatience acts on the sojourn time. We prove a key result, namely, that the state process of the system in the long run converges in distribution to a well-defined Markov process. Closed-form solutions for the probability density function of the virtual waiting time of a queue of type 1 or the offered sojourn time of a queue of type 2 in a given state are derived which are, interestingly, found to depend only on the local state of the queue. The efficacy of the approach is illustrated by some numerical examples.