Study of the delay at traffic signals using an Mt/Mt/1/N queueing model with competition between two types of customers

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We studied vehicle traffic at a signalized intersection using an Mt/Mt/1/N queueing model with two types of customers, who compete for service from a single server. Arrival of vehicles is according to a Poisson process with time-dependent parameter λ(t), and their service time follows an exponential distribution with a time-dependent parameter μ(t). If an approaching customer has to queue, they may join a queue of negative customers instead of the main queue of positive customers. Formation of negative customers occurs from the main Poisson stream according to the following rule: a customer, upon entering the system, decides to join the queue of negative customers with probability δ if the number of negative customers is less than or equal to that of positive customers. When the server is active, at each service completion epoch, a negative customer may forcefully get service with probability β1. Negative customers may thus extend a positive customer’s waiting time and further increase congestion. The bad effect caused by negative customers is studied on the basis of the delayexperienced by different types of customers. We conducted an extensive numerical study based on simulated and real-world data, which includes a comparison of the delays computed by the Mt/Mt/1/N queueing model and those by the incremental queue accumulation (IQA) method.