Institute for Systems Research

Ourfirst contribution is the use of Fair Queueing in conjunction withProbabilistic Fair Drop, a new buffer management policy to allocatebandwidth and buffer space in the gateway, to ensure that all TCPflows threading the gateway achieve high end-to-end throughput andfair service.

Our second contribution is to introduce the concept ofbuffer dimensioning to alleviate the inherent bias of the TCPalgorithm towards connections with large Round Trip Time.

In supportof each of these contributions, we report on extensive simulationresults. Our scheme outperforms other resource allocation schemesreported in the literature and in particular, demonstrates significantimprovements in fairness to long RTT connections in the hybrid networkframework.

We first present an analyticaltechnique to obtain the 'mean' queue occupancy and the 'mean' of the individual TCP windows. Armed with this estimate of the means, wethen derive the window distribution of each individual TCPconnection. Extensive simulation experiments indicate that, under a wide variety of operating conditions, our analytical method is quite accurate in predicting the 'mean' as well asthe distributions. The derivation of the individual distributions is based upon a numerical analysis presented which considers the case of a single TCP flow subject to variable state-dependent packet loss.

Furthermore, in an attempt to capture the past of the sequence, we introduce the negative partial sum processes ${ X_n^{T,-}(cdot),; n=z }$ defined by [ X_n^{T,-}(t)(omega) ~ equiv ~ left{ a{ll} ds {1 over n} {sum_{i=1-ceiling{nt}}^{0} x_i(omega)} & mbox{if} quad ceiling{nt} geq 1 \ 0 & mbox{otherwise} ea ight., quad t in [0,T], quad omega in Omega .

] These processes take value in the space $(D_l[0,T]^p, au_0)$ of, left- continuous functions $[0,T] ightarrow R^p$ with right-hand, limits also equipped with the Skorohod's $J_1$ topology. This paper explores some of the issues associated with, transfering the LDP for the family ${X_n^1 (cdot),~n=z}$ in $(D[0,1]^p, au_0)$ to the families ${X_n^{T}(cdot), ; n=z}$ in $(D[0,T]^p, au_0)$, ${X_n^{T,-}(cdot), ; n=z}$ in $(D_l[0,T]^p, au_0)$ and ${(X_n^T(cdot), X_n^{T,-}(cdot)), ; n=z}$ in $(D[0,T]^p, au_0) x (D_l[0,T]^p, au_0)$ for arbitrary $T>0$; the last two types of transfers require, stationarity of the underlying sequence ${x_n, ; n=pmz}$. The motivation for this work can be found in the study of, large deviations properties for general single server queues, and more specifically, in the derivation of the effective bandwidth, of its output process, all discussed in a companion paper. In a significant departure from the situation under the uniform topology, such transfers are not automatic under the Skorohod topology, as additional continuity properties are required on the elements of, the effective domain of the rate function $I_X$ of the LDP, for ${X_n^1(cdot),~n=z}$ in $(D[0,1]^p, au_0)$.

However, when the rate function $I_X$ is of the usual integral form, the transfers are automatic, and the new rate functions assume, very simple forms suggesting that from the perspective, of large deviations, the past of the underlying stationary process, behaves {it as if} it were independent of its future.

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