Deciding which queue to join: Some counterexamples
Operations Research
Journal of the ACM (JACM)
Optimality of routing and servicing in dependent parallel processing systems
Queueing Systems: Theory and Applications
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
Asymptotic Results and a Markovian Approximation for the M(n)/M(n)/s+GI System
Queueing Systems: Theory and Applications
On Queuing with Customer Impatience until the End of Service
IPDS '00 Proceedings of the 4th International Computer Performance and Dependability Symposium
Operations Research Letters
Fault-aware grid scheduling using performance prediction by workload modeling
The Journal of Supercomputing
A parallel solution for scheduling of real time applications on grid environments
Future Generation Computer Systems
Dynamic routing of real-time jobs among parallel EDF queues: A performance study
Computers and Electrical Engineering
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We consider a queueing system with a number of identical exponential servers. Each server has its own queue with unlimited capacity. The service discipline in each queue is first-come-first-served (FCFS). Customers arrive according to a state-dependent Poisson process with an arrival rate which is a non-increasing function of the number of customers in the system. Upon arrival, a customer must join a server's queue according to a stationary state-dependent policy, where the state is taken to be the number of customers in servers' queues. No jockeying among queues is allowed. Each arriving customer is limited to a generally distributed patience time after which it must depart the system and is considered lost. Two models of customer behavior are considered: deadlines until the beginning of service and deadlines until the end of service. We seek an optimal policy to assign an arriving customer to a server's queue. We show that, when the distribution of customer impatience satisfies certain property, the policy of joining shortest queue (SQ) stochastically minimizes the number of lost customers during any finite interval in the long run. This property is shown to always hold for the case of deterministic customer impatience.