Abstract. Due to their wide area of applications, queueing models with batch service, where the server can process several customers simultaneously, have been studied frequently. An important characteristic of such batch-service systems is the size of a batch, that is the number of customers that are processed simultaneously. In this paper, we analyse a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common first-come-first served single-server queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the number of consecutive same-class customers. After establishing the system equations that govern the system behaviour, we deduce an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. Also, some numerical examples are given that provide further insight in the impact of the different parameters on the system performance.
In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer.
The shift from fossil fuel to more renewable electricity generation will require the broader implementation of Demand Side Response (DSR) into the grid. Utility processes in industry are suited for this, having a large thermal time constant or buffer, and large electricity consumption. A widespread utility system in industry is an induced draft evaporative cooling tower. Considering the safety aspect, such a process needs to maintain cooling water temperature within predefined safe boundaries. Therefore, in this paper, two modelling methods for the prediction of the basin temperature of an induced draft evaporative cooling tower are proposed. Both a white box and a black box methodology are presented, based on the physical principles of fluid dynamics and adaptive neuro-fuzzy interference system (ANFIS) modelling, respectively. By analysing the accuracy of both models with a focus to cooling tower fan state changes, i.e., DSR purposes, it is shown that the white box model performs best. Fostering the idea of using such a system for DSR purposes, the concept of design for flexibility is also touched upon, discussing the thermal mass. Pre-cooling, where the temperature of the cooling water basin is lowered before a fan switch off period, was simulated with the white box model. It was shown that beneficial pre-cooling (to lower the temperature peak) is limited in time.
In many queueing systems the server processes several customers simultaneously. Although the capacity of a batch, that is the number of customers that can be processed simultaneously, is often variable in practice, nearly all batch-service queueing models in literature consider a constant capacity. In this paper, we extend previous work on a batch-service queueing model with variable server capacity, where customers of two classes are accommodated in a common first-come-first-served single-server queue. We include correlation between the classes of consecutive customers, and the service times are geometrically distributed. We establish the equations that govern the system behaviour, the stability condition, and an expression for the steady-state probability generating function of the system occupancy at random slot boundaries. In addition, some numerical results are shown to study the impact of the mean service times and of the customer-based correlation in the arrival process on the performance of the queueing system.
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