Server pooling models for separate and bounded queues

The focus of this paper is on queueing models with arrivals from several sources, where the number of waiting spaces for each arrival source is finite. The main distinction from prior studies is that in our models waiting spaces are separate. Within this context, we examine the benefit of pooling, regardless of whether arrival rates are equal or different. We present a Quasi-Birth-and-Death (QBD) model to address the general case, with simplified versions tailored to specific scenarios. One practical application of the proposed models can be found in the loading and unloading processes at container terminals. We define a measure for stochasticity-related inefficiency, denoted relative interaction delay (RID), and analyze its behavior for the case of a single waiting space for each source. We show analytically that in the base model, the RID approximation is inversely proportional to the number of pooled queues. Numerical evaluations show an added benefit of pooling when arrival rates differ, observing a linear enhancement that is notably more pronounced.