Discrete-time queues with variable service capacity: a basic model and its analysis

Abstract

In this paper, we present a basic discrete-time queueing model whereby the service process is decomposed in two (variable) components: the demand of each customer, expressed in a number of work units needed to provide full service of the customer, and the capacity of the server, i.e., the number of work units that the service facility is able to perform per time unit. The model is closely related to multi-server queueing models with server interruptions, in the sense that the service facility is able to deliver more than one unit of work per time unit, and that the number of work units that can be executed per time unit is not constant over time.Although multi-server queueing models with server interruptions -to some extentallow us to study the concept of variable capacity, these models have a major disadvantage. The models are notoriously hard to analyze and even when explicit expressions are obtained, these contain various unknown probabilities that have to be calculated numerically, which makes the expressions difficult to interpret. For the model in this paper, on the other hand, we are able to obtain explicit closed-form expressions for the main performance measures of interest. Possible applications of this type of queueing model are numerous: the variable service capacity could model variable available bandwidths in communication networks, a varying production capacity in factories, a variable number of workers in an HR-environment, varying capacity in road traffic, etc.

Effect of Parameters on Geoa/Geob/1 Queues: Theoretical Analysis and Simulation Results

“…The steady-state distribution, if it exists, must be a particular solution of Equation (13). The general solution of Equation (13) is…”

“…Bruneel et al [12] examine the model with fixed service capacity, while in [13] they consider systems with variable service capacity. Focusing in the interval between arrivals (keeping it constant) and constant time of service, Zhao and Campbell [14] use the roots, both inside and outside the unit circle, of the denominator of the generating function for the system D X /D m /1.…”