Analysis of an Asymmetric Polling Model with Cycle-time Constraint

Abstract

Local area networks (LANs) have been extensively constructed to efficiently serve nonreal-time traffic such as data traffic. Due to the multiplexing techniques for multi-media communications, it is required to integrate nonreal-time traffic which tolerates possibly long delay and real-time traffic (e.g.,voice,video) which poses strict delay constraint. However ordinary LAN protocols cannot adequately meet this requirement.

The FDDI protocol employs a token passing scheme with cycle-time constraint, which limits the amount of nonreal-time traffic transmitted by a station to preserve smooth transmission of real-time traffic. With the scheme, real-time traffic is guaranteed to be transmitted within predetermined delay and nonreal-time traffic is transmitted unless its transmission causes real-time traffic excessive delay. Most works related to a token passing scheme with cycle-time constraint have investigated the allocation of bandwidth. Mean waiting time for messages in a symmetric system is analyzed by Takagi, but no asymmetric system has been analyzed yet.

In our study, we consider the mathematical model for a token passing scheme with cycle-time constraint and analyze waiting time for messages in an asymmetric system, where each message arrives according to a Poisson process. Service time and switchover time are constant, so that we can discretize time axis. Each station can transmit a message unless it causes excessive delay of real-time traffic. We consider the case where the load of each station may differ and the restriction on token rotation time at each station may differ. From the numerical results, it turns out that the mean message waiting time depends on the location of the station, and that the saturation point of load at which each queue becomes unstable depends on the selection of target token rotation time.