Fundamentals of queueing theory (2nd ed.).
Fundamentals of queueing theory (2nd ed.).
On the M(n)/M(n)/s queue with impatient calls
Performance Evaluation
On queueing with customer impatience until the beginning of service
Queueing Systems: Theory and Applications
M/M/1 Queue with Impatient Customers of Higher Priority
Queueing Systems: Theory and Applications
The Virtual Waiting Time of the M/G/1 Queue with Impatient Customers
Queueing Systems: Theory and Applications
Busy Periods of Poisson Arrival Queues with Loss
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
Stationary delays for a two-class priority queue with impatient customers
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
On priority queues with impatient customers
Queueing Systems: Theory and Applications
Probability in the Engineering and Informational Sciences
The stationary workload of the G/M/1 queue with impatient customers
Queueing Systems: Theory and Applications
Simulation model for extended double-ended queueing
Computers and Industrial Engineering
Dynamic fluid-based scheduling in a multi-class abandonment queue
Performance Evaluation
Computers and Electrical Engineering
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The paper deals with the two-class priority M/M/1 system, where the prioritized class-1 customers are served under FCFS preemptive resume discipline and may become impatient during their waiting for service with generally distributed maximal waiting times. The class-2 customers have no impatience. The required mean service times may depend on the class of the customer. As the dynamics of class-1 customers are related to the well analyzed M/M/1+GI system, our aim is to derive characteristics for class-2 customers and for the whole system. The solution of the balance equations for the partial probability generating functions of the detailed system state process is given in terms of the weak solution of a family of boundary value problems for ordinary differential equations, where the latter can be solved explicitly only for particular distributions of the maximal waiting times. By means of this solution formulae for the joint occupancy distribution and for the sojourn and waiting times of class-2 customers are derived generalizing corresponding results recently obtained by Choi et al. in case of deterministic maximal waiting times. The latter case is dealt as an example in our paper.