Fast Algorithms for TVAR and MTIE Computation in Characterization of Network Synchronization Performance

Time Variance (TVAR) and Maximum Time Interval Error (MTIE) are historically the main time-domain quantities for the specification of network synchronization performance in telecommunications standards. Nevertheless, plain computation of the TVAR and MTIE standard estimators proves cumbersome in most cases of practical interest, due to their heavy computational weight. In this paper, TVAR and MTIE are first introduced according to their standard definitions. Then, fast algorithms based on recursion and on binary decomposition to compute the TVAR and MTIE standard estimators are provided, which effectively cut down the number of operations needed. The MTIE algorithm based on binary decomposition reduces the number of operations needed to a term proportional to Nlog2N instead of N2. Both algorithms allow fast evaluation in most practical situations: even very long sequences of TE samples do not require more than few seconds of data processing for TVAR and MTIE computation. Key-Words: clocks, digital communication, jitter, MTIE, SDH, SONET, synchronization, TVAR, wander.