Heavy traffic analysis of a queueing system with bounded capacity for two types of customers

We study a service system with a fixed upper bound for its workload and two independent inflows of customers: frequent ‘small’ ones and occasional ‘large’ ones. The workload process generated by the small customers is modelled by a Brownian motion with drift, while the arrival times of the large customers form a Poisson process and their service times are exponentially distributed. The workload process is reflected at zero and at its upper capacity bound. We derive the stationary distribution of the workload and several related quantities and compute various important characteristics of the system.