Joint pushing and proactive caching holds the promise of significantly increasing the throughput and decreasing the latency of content-centric wireless networks. In this work, we import the pushing and caching mechanism into a traditional packet-oriented network for decreasing the average queueing delay. Since the decreasing relies on extra costs paid for the pushing-caching mechanism, such as the cost for the cache buffer's capacity, extra transmission power for pushing and so on, we mainly derive the average queueing delay under given cost in order to study the relationship between the average queueing delay and the extra cost. In order to do so, a metric named System State is defined to describe the transmitter and user's current buffer states. Based on the System State, a two-dimensional Markov Chain is built to derive the average queueing delay and the average hitting ratio. The results show us how much the average queueing delay can achieve when the cache buffer's capacity which usually has a high cost is given, and then provide us a method to make a tradeoff between the average queueing delay and the cost of the user's buffer size. Simulation results validate our conclusion.