A GI (A, B/(A,Q)) /D/ 1/Qmax Queue Approach for the Estimation of the Proportion of a Deteriorated Length of a Road Network

Abstract

This article proposes a simple methodology for the classification of road segments of a highway into a set S={0, 1, 2 , …, Qmax} of states. A GI(A, B/(A,Qmax)/D/1/Qmax queueing approach, estimates the length of a deteriorated/damaged portion of a road network which requires reconstruction for a better riding comfort which is measured in terms of multiples of the service period. One unit of service time is defined by a pavement management system (PMS) monitoring the queue aspects as an hour or a day needed to reconstruct a length of ‘D’ kilometers (km) of a damaged portion of a road segment; i.e. the service time here is deterministic. The entire coded length of the highway in terms of the maximum discrete service period is Qmax which means that the real length of the highway under study is (DQmax) km. Here, the inter-arrival time ‘A’ between consecutive batch arrival of damages and the size of a number ‘B’ of units of damaged portion arrived are measured as multiples of the single service time. Treating the sequence {tn; n [0,1,2,…}} of arrival epochs as renewal points of the queue occupancy process Q(t), the queueing number of damaged units of road length at time ‘t’, this queueing problem is investigated further using the embedded Markov Chain (MC) methods.