Delay analysis of a discrete‐time multiclass slot‐bound priority system

This paper introduces a new priority mechanism in discrete‐time queueing systems that compromises between first‐come‐first‐served (FCFS) and head‐of‐line priority. In this scheduling discipline–which we dubbed slot‐bound priority–customers of different priority classes entering the system during the same time‐slot are served in order of their respective priority class. Customers entering during different slots are served on a FCFS basis. In this paper we study the delay in an N‐class discrete‐time queueing system under slot‐bound priority. General independent arrivals and class‐specific general service time distributions are assumed. Expressions for the probability generating function of the delay of a random type‐j customer are derived, from which the respective moments are easily obtained. The tail behaviour of these distributions is analyzed as well, and some numerical examples show the effect slot‐bound priority can have on the performance measures.