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Emergence of new types of services has led to various traffic and diverse delay requirements in fifth-generation (5G) wireless networks. Meeting diverse delay requirements is one of the most critical goals for the design of 5G wireless networks. Though the delay of point-to-point communications has been well investigated, the delay of multi-point to multi-point communications has not been thoroughly studied, since it is a complicated function of all links in the network. In this paper, we propose a novel tractable approach to analyze the delay in the heterogeneous cellular networks with spatio-temporal random arrival of traffic. Specifically, we propose the notion of delay outage and evaluate the effect of different scheduling policies on the delay performance. Our numerical analysis reveals that offloading policy based on the cell range expansion greatly reduces the macrocell traffic, while bringing a small amount of …