A Two-Queue Polling Model with Two Priority Levels in the First Queue

Abstract

In this paper we consider a single-server cyclic polling system consisting of two queues. Between visits to successive queues, the server is delayed by a random switch-over time. Two types of customers arrive at the first queue: high and low priority customers. For this situation the following service disciplines are considered: gated, globally gated, and exhaustive. We study the cycle time distribution, the waiting times for each customer type, the joint queue length distribution at polling epochs, and the steady-state marginal queue length distributions for each customer type.

Analysis and performance comparison of uniform and mixed service policy for vacation queue

“…In our work we have incorporated p 1 and p 2 in equations (III.14a). In [8] we find that the term ρL 1−ρH represents the fraction of time that the server is busy with cycle started by type-L customers when there are no more type-H customers in the system. We have multiplied this probability with the fraction of type-L customers that occupies the system.…”

“…Adan, et.al. in [8]. The authors [8] have considered all the queues including all the types of customers inside the same queue followed similar service like globally gated, gated and exhaustive.…”

“…The authors [8] have considered all the queues including all the types of customers inside the same queue followed similar service like globally gated, gated and exhaustive. The limitation of [8] is, mixed of exhaustive and gated policy is not considered within a queue who having two types of traffic arriving. Our present paper is an extension of our previous work [7] considering a mixed service policy in comparison with [8].…”

“…The limitation of [8] is, mixed of exhaustive and gated policy is not considered within a queue who having two types of traffic arriving. Our present paper is an extension of our previous work [7] considering a mixed service policy in comparison with [8]. The difference with [8] is that, we have considered a mixed service comprised of exhaustive and gated vacation policy for the first queue, where in [8] an uniform service of either exhaustive or gated policy has been followed.…”

A mixed service for two queue gated vacation with Bernoulli schedule policy

“…Once the cycle time distribution at the beginning of n-th polling epoch for type-1 customers is obtained, we can compute the LST of waiting time by following the method described in [11]. In the previous section, we have shown the computation of n-th cycle time from (n-1)-th cycle time.…”