Estimating percent-time-spent-following on two-lane rural highways Moshe Cohen a,⇑ , Abishai Polus b a Department of Industrial Engineering, Jerusalem College of Engineering, Schreibau Street, Jerusalem, Israel b Department of Civil and Environmental Engineering, Technion, Haifa 32000, Israel article info Article history: Received 8 February 2010 Received in revised form 13 March 2011 Accepted 14 March 2011 Keywords: Highways Rural Two-lane PTSF Queuing abstract This study concentrated on estimating the percent-time-spent-following (PTSF) on two- lane highways. This measure is a key estimate of level-of-service in traffic engineering applications. Its evaluation to date has been based on simulations that yielded over- estimated values. The present study shows how to estimate this variable from easily obtained field data based on queuing theory. The estimates accord with opinions on yield- ing significantly lower values of PTSF that are expressed in the relevant traffic literature. An improved relationship between PTSF and two-way flow is provided by fitting the new estimates by means of the least-squares method. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The level-of-service concept is commonly accepted in traffic engineering as a way to evaluate the quality and character- istics of flow on various facilities. For example, it is needed for decision-making on adding lanes, re-aligning highways and conducting safety analyses. This paper shows that utilizing relatively simple operations research methodologies may con- tribute directly to advancing important traffic engineering issues that have not previously been explored. One of the recommended measures of the level-of-service of two-lane rural highways, according to the leading manual of traffic analysis, the Highway Capacity Manual (HCM, 2000), is the proportion of time that fast vehicles travel in platoons be- hind slow vehicles. This proportion is typically measured by the Percentage of Time Spent Following (PTSF). In reality, it is rather difficult to measure PTSF because of the complexity of collecting data for fast-traveling vehicles that follow slower vehicles. This means that direct measurement, which would also necessitate the use of complicated equipment would be prohibitively expensive, if not practically impossible, to make. An alternative would be to calculate PTSF from simulation runs; however, this approach has disadvantages, mainly because it requires assumptions regarding traffic characteristics, particularly the behavior of drivers in passing maneuvers. Previous studies have not provided other alternative analytical approaches for calculating PTSF values. The present research offers a theoretical model to determine PTSF values for different flow conditions from readily available and easily observed traffic data. The new model provides values that are significantly lower than the HCM model, which is known to be overestimated (e.g., Harwood et al., 2003; Luttinen, 2001). A few assumptions must be made to arrive at an analytical model to estimate PTSF. Although these simplifying assump- tions are not often fulfilled, they are fairly close to reality in some conditions. Without any assumptions, it becomes impos- sible to solve the model analytically; the assumptions in this work are necessary to derive a theoretical formula whose arguments are easily measurable quantities. Furthermore, it will be shown that the results of the model’s predictions of PTSF provide values that are lower than the HCM values. 0968-090X/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.trc.2011.03.001 ⇑ Corresponding author. E-mail addresses: bani@jce.ac.il (M. Cohen), polus@technion.ac.il (A. Polus). Transportation Research Part C 19 (2011) 1319–1325 Contents lists available at ScienceDirect Transportation Research Part C journal homepage: www.elsevier.com/locate/trc