• Journal of the Korean Operations Research and Management Science Society
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• v.22 no.1
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• pp.101-121
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• 1997

Consider a Jackson type closed queueing network in which each queue has a single exponential server. Assume that N customers are moving among .kappa. queues. We propose a candidata procedure which yields a lower bound of the network throughput which is sharper than those which are currently available : Let (.rho.$_{1}$, ... .rho.$_{\kappa}$) be the loading vector, let x be a real number with 0 .leq. x .leq. N, and let y(x) denote that y is a function of x and be the unique positive solution of the equation. .sum.$_{i = 1}$$^{\kappa}$y(x) .rho.$_{i}$ (N - y(x) x $p_{i}$ ) = 1 Whitt [17] has shown that y(N) is a lower bound for the throughput. In this paper, we present evidence that y(N -1) is also a lower bound. In dosing so, we are led to formulate a rather general conjecture on 'quot;Migrating Critical Points'quot; (MCP). The .MCP. conjecture asserts that zeros of successive derivatives of certain rational functions migrate at an accelerating rate. We provide a proof of MCP in the polynomial case and some other special cases, including that in which the rational function has exactly two real poles and fewer than three real zeros.tion has exactly two real poles and fewer than three real zeros.

• Journal of KIISE:Information Networking
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• v.29 no.2
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• pp.147-155
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• 2002

Seamless connection can be a good solution to reduce processing delays in interworking points, a possible big burden to the data transmission in Internet. This paper, therefore, will present several interworking methods which can minimize the delays through seamless connections in interworking between MPOA networks, usually ATM-LANs, and MPLS networks, mainly Internet backbones. We compare characteristics of those networks, propose requirements for interworking, and describe three Interworking methods. Proposed Interworking methods reduce end-to-end transmission delay for seamless connection between ATM VC and LSP, as decreases the number of IP lookup processing in LER. We describe detailed process and characteristic of each interworking method, And we analyze and compare end-to-end delay, using Jackson's network theorem, of proposed interworking methods.