Article Contents
Article Contents

# Stability of a queue with discriminatory random order service discipline and heterogeneous servers

• * Corresponding author: Bara Kim
• We consider a queueing system with two classes of customers, two heterogeneous servers, and discriminatory random order service (DROS) discipline. The two servers may have either the same or different DROS weights for each class. Customers of each class arrive according to a Poisson process and the service times of each class of customers are assumed to be exponentially distributed with service rate depending on both the customer's class and the servers. We provide stability and instability conditions for this two-class two-server queue with DROS discipline.

Mathematics Subject Classification: Primary: 60K25; Secondary: 60J27.

 Citation:

• Figure 1.  The curve dividing the two regions

Figure 2.  The stable and unstable regions of Example 1 (when $\mu_{11}=0.9$, $\mu_{12}=0.1$, and $\mu_{21}=\mu_{22}=0.5)$

Figure 3.  Simulation results for $N_1(t)$ and $N_2(t)$ in Example 1 (when $\mu_{11}=0.9$, $\mu_{12}=0.1$, $\mu_{21}=\mu_{22}=0.5$, and $\lambda_1=\lambda_2=0.5$)

Figure 4.  The curve dividing the stable and unstable regions

Figure 5.  The stable and unstable regions of Example 2 (when $\mu_{11}=0.9$ and $\mu_{12}=0.1$)

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