On the Modeling of Voice Packet Loss in FIFO Switches

In this talk, we propose the average renewal cycle (ARC) model to estimate packet loss probability for on-oo traac sources in a statistically mul-tiplexed rst-in-rst-out (SMF) switch. SMF is a widely adopted architecture for switches, routers, and many other types of communications devices. In ARC, a worst case scenario on the cell loss process is derived for aggregated traac states, so that we can derive an upper bound for the cell loss probability at the output buuer of the ATM switch. For homogeneous sources, the computational complexity to estimate cell loss probability through the ARC model is O(n+A s +M), where n is the number of connections, A s is the average number of cells arrived in overload period and M is the buuer size. The packet loss probability derived from this model is higher, but very close to the simulation results, making it suitable for real-time admission control of voice channels. A bursty packet source can be modeled as a time-dependent stochastic process, i.e., the Modulated Markovian Process (MMP), where each of its states represents a diierent packet generation ratee1, 2]. When packets sent by several bursty sources are multiplexed in an SMF switch, the packet loss probability in the SMF output queue can be solved by an MMP/D/1/M queuing model. However, the computation of this model grows exponentially with buuer size, making it necessary to use other simpler approximation models for on-line network management applications 3, 4, 5, 6, 7], provided that the estimation is fast, yet conservative model, such as ARC. A voice source is modeled by two states, on (active) or oo (inactive). When at an \on" state, the source generates packets at a random rate. Otherwise, the source does not generate any packet. When a buuer is full, newly arrived packets are dropped according to certain prioritiza-tion schemes. Relevant performance parameters of a source include: 1) peak packet generation rate , 2) the average duration of the on-state (or burst length) T b , and 3) the source utilization , which is deened as the ratio of its average packet generation rate and the peak rate. Ts+T b , where T s is the average duration of the silence period of the source. The sojourn times of \on" and \oo" states are exponentially distributed. When a source is at its on-state, it generates packets based on an exponential distribution at a given rate. Without loss …