Stochastic Models for Throughput Analysis of Randomly Arriving Elastic Flows in the Internet

Abstract

This paper is ahnut analytical mndels fnr calculating the aver-age handwidth shares nhtained hy TCP cnntrnlled finite file transfers that arrive randnmly and share a single (bottleneck) link. Owing tn the complex nature nf the TCP cnngestinn cnntrnl algnrithm, a single mndel dries nnt wnrk well fnr all cnmhinatinns nf netwnrk parameters (i.e., mean file size, link capacity, and prnpagatinn delay). We prnpnse twn mndels, de-velnp their analyses, and identify the reginns nf their applicability. One mndel is nhtained frnm a detailed analysis nf TCP’s AIMD adaptive win-dnw mechanism; the analysis accnunts fnr sessinn arrivals and departures, and finite link buffers. It is essentially a Prncessnr Sharing (PS) mndel with time varying service rate; hence we call it TCP-PS. The nther mndel is a simple mndificatinn nf the PS mndel that accnunts fnr large prnpagatinn delays; we call this mndel Rate Limited-PS (RL-PS). The TCP-PS mndel analysis accnmmndates a general file size distrihutinn hy apprnximating it with a mixture nf expnnentials. The RL-PS mndel can he used fnr general file size distrihutinns. We shnw that the TCP-PS mndel cnnverges tn the standard PS mndel as the prnpagatinn delay apprnaches zern. We alsn nhserve that the PS mndel prnvides very pnnr estimates nf thrnughput unless the prnpagatinn delay is very small. We nhserve that the key parameters affecting the thrnughput are the handwidth delay prnduct (BDP), file size distrihutinn, the link buffer and the traffic intensity. Several numerical cnmparisnns between analytical and simulatinn re-sults are prnvided. We nhserve that the TCP-PS mndel is accurate when the BDP is small cnmpared tn the mean file size, and the RL-PS mndel wnrks well when the BDP is large cnmpared tn the mean file size.

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