Original scientific paper
https://doi.org/10.17535/crorr.2027.0011
Study of the delay at traffic signals using an $M_t/M_t/1/N$ queueing model with competition between two types of customers
Reya Kuruvila
orcid.org/0000-0002-7025-9638
; Department of Mathematics, Rajagiri School of Engineering & Technology, Rajagiri Valley, Kochi, Kerala, India; Department of Mathematics, Govt. Engineering College, Thrissur, Kerala, India; and APJ Abdul Kalam Technological University, CET Campus, Thiruvananthapuram, Kerala, India,
Narayanan C. Viswanath
; Department of Mathematics, Govt. Engineering College, Thrissur, Kerala, Indiaand APJ Abdul Kalam Technological University, CET Campus, Thiruvananthapuram, Kerala, India
*
* Corresponding author.
Abstract
We studied vehicle traffic at a signalized intersection using an $M_t/M_t/1/N$ 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 $\lambda(t)$, and their service time follows an exponential distribution with a time-dependent parameter $\mu(t)$. 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 $\delta$ 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 $\beta_1$. 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 delay experienced 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 $M_t/M_t/1/N$ queueing model and those by the incremental queue accumulation (IQA) method.
Keywords
$M_t/M_t/1/N$ queueing model; incremental queue accumulation method; negative customers; external uniformization method; traffic delay
Hrčak ID:
352449
URI
Publication date:
26.10.2026.
Visits: 0 *