Performance analysis of a continuous-time two-class global first-come-first-served queue with two servers and presorting

This paper considers a continuous-time queueing model with two types (classes) of customers each having their own dedicated server. The objective is to have a better grasp on the concept of a global first-come-first-served service discipline with presorting, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their type, with an exception of the firstPcustomers. For the firstPcustomers the FCFS rule holds only within the type, i.e., customers of different types can overtake each other in order to be served. Due to the global FCFS rule the model becomes non-workconserving and on the other hand we also have to keep track of the types of customers in the firstPcustomers. The motivation of our work is the concept of a turn lane in road traffic, i.e., a lane reserved for vehicles making a specific turn at the next junction. This paper intends to be a step towards an analytic model to aid in the decision process of various policy makers of the optimal length of turn lanes.