Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

Abstract

We consider discouraged arrival of Markovian queueing systems whose service speed is regulated according to the number of customers in the system. We will reduce the congestion in two ways. First we attempt to reduce the congestion by discouraging the arrivals of customers from joining the queue. Secondly we reduce the congestion by introducing the concept of service switches. First we consider a model in which multiple servers have three service rates μ 1, μ 2, and μ (μ 1 ≤ μ 2