Delay Analysis for Triggered Requests: M/G/1 Modeling Approach

摘要

In many communication networks, the transmission of one packet might automatically trigger the transmission of a subsequent packet from the same source after some delay, without requiring acknowledgment or feedback on the status of the primary transmission. Traditional queueing models, assuming independent interarrival times, fail to model such a scenario. In this paper, we analyze a single-server queue with two classes: primary customers arriving via a Poisson process, and secondary customers triggered by primary ones after a random delay. Both have i.i.d. exponential service times. We show that secondary customers see the queue either in steady state or with one extra customer. Based on this, we propose an analytical approach that models secondary arrivals as an independent Poisson process with an effective service time, consisting of an exponential distribution (probability p) and an Erlang-2 distribution (probability 1− p). Consequently, the primary arrival process is thinned by p. The system is modeled as a multi-class M/G/1 queue, enabling the computation of p and the Laplace-Stieltjes transform of the system time. Simulations confirm the high accuracy of our model, particularly for average system time.