On estimating the coverage length of toll collection area and client-server response time

The electronic toll collection system is widely applied to payment collection oo the freeway all over the world. We derive the relationship of the coverage length of the toll collection area m, the vehicle velocity v, and the mean vehicle residence time 1/η. In addition, the processing time of the client system is bounded by the factors of the mean vehicle dwell time, the propagation delay, and the transmission time. The upper bound of the server response time is calculated from the mean response time of the client system, the propagation delay, the transmission time, and the mean vehicle dwell time. Furthermore, the statistical probability bound for the response time performance of the server has been defined by the specified response time for the client system and the acceptable significance level of loss of service p in advance. Finally, the M/M/z queueing simulation estimates the number of server z required for the stringent performance requirement