On the overflow process from a finite Markovian queue
Performance Evaluation
Bound hierarchies for multiple-class queuing networks
Journal of the ACM (JACM) - The MIT Press scientific computation series
Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Simple bonds for finite single-server exponential tandem queues
Operations Research
On Evaluating the Cumulative Performance Distribution of Fault-Tolerant Computer Systems
IEEE Transactions on Computers
Calculating transient distributions of cumulative reward
Proceedings of the 1995 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Performability modelling tools and techniques
Performance Evaluation
Bounding errors introduced by clustering of customers in closed product-form queuing networks
Journal of the ACM (JACM)
Exponential bounds with applications to call admission
Journal of the ACM (JACM)
Traffic overflow in loss systems with selective trunk reservation
Performance Evaluation
Approximation for overflow moments of a multiservice link with trunk reservation
Performance Evaluation
An equivalent random method with hyper-exponential service
Performance Evaluation
Traffic conditioner: upper bound for the spacer overflow probability
Performance Evaluation
Approximating multi-skill blocking systems by hyperexponential decomposition
Performance Evaluation
Asymptotics of overflow probabilities in Jackson networks
Operations Research Letters
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Finite loss queues with overflow naturally arise in a variety of communications structures. For these systems, there is no simple analytic expression for the loss probability. This paper proves and promotes easily computable bounds based on the so-called call packing principle. Under call packing, a standard product form expression is available. It is proven that call packing leads to a guaranteed upper bound for the loss probability. In addition, an analytic error bound for the accuracy is derived. This also leads to a secure lower bound. The call packing bound is also proven to be superior to the standard loss bound. Numerical results seem to indicate that the call packing bound is a substantial improvement over the standard loss bound and a quite reasonable upper bound approximation. The results seem to support a practical usefulness.