Refined Asymptotic Approximations to Loss Probabilities and Their Sensitivities in Shared Unbuffered Resources

• Published in: SIAM journal on applied mathematics 1998-01, Vol.59 (2), p.494-513
• Main Authors: Morrison, John A., Ramakrishnan, K. G., Mitra, Debasis
• Format: Article
• Language: English
• Subjects: Approximation; Broadband transmission; Case studies; Cost control; Critical loading; Design optimization; Freight traffic; Implicit costs; Mathematical integrals; Network management systems; Queueing networks; Recursion; Route optimization; Traffic
• ISSN: 0036-1399; 1095-712X
• DOI: 10.1137/s0036139997326478

We consider an unbuffered resource having capacity C, which is shared by several different services. Calls of each service arrive in a Poisson stream and request a fixed, integral amount of capacity, which may depend on the service. An arriving call is blocked and lost if there is not enough capacity. Otherwise, the capacity of the call is held for the duration of the call, and the holding period is generally distributed. It is assumed that C and the traffic intensities of the services are commensurately large and asymptotic approximations are obtained for the loss probabilities and their sensitivities to the traffic intensity of each service. These sensitivities are important in optimizing the performance of multiservice, multirate loss networks. Numerical results illustrate the accuracy of the asymptotic approximations. These results show that while prior asymptotic approximations to the loss probabilities are quite accurate, the new approximations are very accurate. Moreover, while the prior asymptotic approximations to the sensitivities are overall rather poor, the new approximations are very good. Experience with case studies has shown that computationally efficient asymptotic techniques are crucial to cope with the size and the number of service offerings of emerging broadband networks in their design and optimization.