A New Analytical Approach for Delay Analysis in the Presence of Correlated Arrivals

Correlated demands are commonly encountered in many communication scenarios, e.g., caching networks. In this paper, we propose a new analytical model for considering the effect of correlated arrivals on the average response time in a simple queue with exponential service time. To this end, we consider two types of arrivals, independent and dependent, where the arrival instant of each dependent customer relies on the arrival instant of its companion independent customer. The correlation between these two customer types is determined by a delay between their arrival instants. We explore two correlation scenarios, one where there is no delay, i.e., batch arrival, and another where there is a random delay with a known distribution. To accurately model the correlation impact between arrivals, our model considers some extra arrivals (i.e., redundant arrivals) that can compensate for the impact of the correlation. We demonstrate the validity of our analytical modeling approach analytically in the first correlation scenario and through simulation in the second one. Our proposed model can be used in various communication scenarios for system performance analysis.