Global Conference on Mathematics and Applications (GCMA)

Abstract:
This study investigates a multi-server queueing system with working vacations, waiting servers, and customer impatience. A Bernoulli schedule is considered to model the interruption of working vacations, during which customers are served at a lower service rate. The matrix-geometric method is employed to analyze the steady-state behavior of the system and derive several important performance measures. Numerical results are presented to evaluate the system performance under different operating conditions. In addition, a cost-revenue-profit analysis is conducted to assess the economic efficiency of the system. The proposed model is motivated by its application to call center operations, where service efficiency and customer impatience play a significant role.

Keywords: cost model, differentiated working vacation, matrix analytic method, queueing models.

Steady-state probability distribution:
Let $ L(t) $ represent the number of customers in the system at time $ t $, and let $ S(t) $ denote
the status of the servers at time t. For the mathematical representation of the proposed
model at an instant $ t $, we consider the following states of the system based on the status
of the servers:
[
S(t)=
\begin{cases}
0, & \text{for regular busy period};\
1, & \text{for type-1 working vacation};\
2, & \text{or type-2 working vacation}.
\end{cases}
]