A dynamic prioritization policy for the callback option in a call center

In this paper, we study the $$M_n/M_n/c/(K_1+K_2)+M_n$$ system with two finite-size queues where underlying exponential random variables have state-dependent rates. When all servers are busy, upon arrival customers may join online or offline/callback queue simply balk. Customers waiting in impatient and if their patience expires, they choose to callback instead of abandoning for good. assumed be patient. served following a threshold policy: when number surpasses level, next customer serve is picked from here. Otherwise, only after predetermined agents reserved future arrivals, remaining can served. We conduct an exact analysis obtain its steady-state performance measures. The times spent both expressed as Phase-type distributions. With numerical examples, present how policy responds shorter promised characteristics vary.