First-come-first-served polling systems

One criterion for operating a polling system is the fairness. In most of the polling systems, the fairness is considered on queues. We serve the queue with more customers first or serve more in that queue. The fairness on individual customers has not been considered yet. On the other hand, the service constraints among customers in different queues are also not considered. However, in some system we cannot start the service of a customer until the services of some other customers have been completed. The simplest case is the first-come-first-served (FCFS) system. In this paper, we study polling systems in which customers are served by the basic fairness criterion: first-come-first-served. Both of the central-controlled and distributed systems are investigated. In a central-controlled polling system, the server can always obtain the arrival times of customers and it is easy for him to fulfill the FCFS criterion. However, in a distributed polling system, the server must obtain those arrival times by himself. By assuming that every arriving customer will receive a time-stamp recording his arriving time, we propose a semi-dynamic polling policy. According to this policy, the server can serve customers on the FCFS basis. By relating our systems to an M/G/1 queue with vacations, the average waiting times in queue for both systems are studied.