Title: Computation of delay at traffic signals using an M_t/M_t/1 queueing model

Authors: Kuruvila Reya; Narayanan C. Viswanath

Addresses: Department of Mathematics, Govt. Engineering College, Thrissur, Kerala, India; APJ Abdul Kalam Technological University (CET Campus), Thiruvananthapuram, Kerala, India ' Department of Mathematics, Govt. Engineering College, Thrissur, Kerala, India; APJ Abdul Kalam Technological University (CET Campus), Thiruvananthapuram, Kerala, India

Abstract: Several formulae/methods exist in the literature to compute delay at traffic signals. Among these, the Incremental Queue Accumulation (IQA) model can be considered a universal model in that the vehicle arrival and departure rates are the only parameters required for its computation. In the IQA model, the vehicle queue length computation uses a deterministic model. This paper presents a variant of the IQA model, in which the queue length is computed using the transient probability distribution of an M_t/M_t/1 queueing model. The average and total delay are defined similarly to the IQA model. The performance of the new average delay model was compared to that of five existing average delay formulae, including the IQA delay, based on real and simulated traffic data. This study shows that the new model outperforms the existing delay models when the overflow queue sizes are high.

Keywords: delay at traffic signals; queueing model; time-dependent rates; cycle time.

DOI: 10.1504/IJVICS.2026.152936

International Journal of Vehicle Information and Communication Systems, 2026 Vol.11 No.2, pp.180 - 196

Received: 17 May 2024
Accepted: 12 May 2025
Published online: 15 Apr 2026 *

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