Routing and capacity allocation in networks with trunk reservation
Mathematics of Operations Research
A critically loaded multiclass Erlang loss system
Queueing Systems: Theory and Applications
Multiservice Loss Models for Broadband Telecommunication Networks
Multiservice Loss Models for Broadband Telecommunication Networks
Prioritized resource allocation for stressed networks
IEEE/ACM Transactions on Networking (TON)
Optimal capacity planning in stochastic loss networks with time-varying workloads
Proceedings of the 2007 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Assessing the efficiency of resource allocations in bandwidth-sharing networks
Performance Evaluation
Multiserver Loss Systems with Subscribers
Mathematics of Operations Research
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We consider a loss system model of interest in telecommunications. There is a single service facility with N servers and no waiting room. There are K types of customers, with type i customers requiring A_i servers simultaneously. Arrival processes are Poisson and service times are exponential. An arriving type i customer is accepted only if there are R_i \,(\geq A_i ) idle servers. We examine the asymptotic behavior of the above system in the regime known as critical loading where both N and the offered load are large and almost equal. We also assume that R_1,\ldots, R_{K-1} remain bounded, while R^N_K\to\infty and R^N_K/\sqrt{N}\to0 as N \to\infty. Our main result is that the K dimensional “queue length” process converges, under the appropriate normalization, to a particular K dimensional diffusion. We show that a related system with preemption has the same limit process. For the associated optimization problem where accepted customers pay, we show that our trunk reservation policy is asymptotically optimal when the parameters satisfy a certain relation.