Traffic congestion is observed around shopping malls, mostly, due to the long queue at the parking entry gates. The queuing theory is an operation research technique that mathematically models the queuing systems consisting of randomly arriving costumers to receive service and then depart such as the parking entry gates. For a single-server mathematical queuing model, the inter-arrival time is usually assumed to be negative exponentially distributed (Poisson process). Mostly, the service times are assumed to be either similar to inter-arrival, M/M/1, or constant, M/D/1; neither assumptions is correct in terms of producing performance measures that conform with the reality. However, the M/D/1 model seems to perform more closely. This paper proposes an approach to apply the mathematical queuing model for such system more efficiently. Essentially, service time is calibrated to the best fitting distribution based on the data collected from major shopping malls in Alexandria and Giza in 2016 and 2017; respectively. The calibration proves that the service time is normally distributed. The application of the M/D/1 using the mean time of the calibrated normal distribution as the constant service time is then tested. The resulted performance measures show a significant conformity with the performance measures of the field data.

大型购物中心由于在停车场入口门口排长队而导致交通拥堵。排队理论是一种运筹学技术，可以对由随机到达的顾客组成的排队系统进行数学建模，以接受服务，然后从停车入口门等出发。对于单服务器数学排队模型，到达时间通常假定为负指数分布（泊松过程）。通常，服务时间被假定为类似于到达间隔M / M / 1，或者是恒定M / D / 1。就制定符合实际情况的绩效指标而言，这两种假设都不正确。但是，M / D / 1模型似乎表现得更紧密。本文提出了一种将数学排队模型更有效地应用于此类系统的方法。本质上，根据2016年和2017年从亚历山大和吉萨的主要购物中心收集的数据，将服务时间校准为最佳拟合分布; 分别。校准证明服务时间是正态分布的。然后测试使用校准的正态分布的平均时间作为恒定服务时间的M / D / 1的应用。所产生的性能指标表明与现场数据的性能指标有很大的一致性。