GPU-accelerated computing is a key technology to realize high-speed inference servers using deep neural networks (DNNs). An important characteristic of GPU-based that the computational efficiency, in terms processing speed and energy consumption, drastically increases by multiple jobs together batch. In this paper, we formulate as batch service queueing model with batch-size dependent times. We...

We obtain the queue length probability distribution at equilibrium for a multi-server, single queue with generalised exponential (GE) service time distribution and a Markov modulated compound Poisson arrival process (MMCPP)—i.e. a Poisson point process with bulk arrivals having geometrically distributed batch size whose parameters are modulated by a Markovian arrival phase process. This arrival...

In many service industries, the firm adjusts the product price dynamically by taking into account the current product inventory and the future demand distribution. Because the firm can easily monitor the product inventory, the success of dynamic pricing relies on an accurate demand forecast. In this paper, we consider a situation where the firm does not have an accurate demand forecast, but can...

Discrete-time queueing models find a large number of applications as they are used in modeling systems arising digital platforms like telecommunication and computer networks. In this paper, we analyze an infinite-buffer model with discrete Markovian arrival process. The units on served batches by single server according to the general bulk-service rule, service time follows distribution rate de...

In this paper we present new analytical results concerning long-term staffing problem in high-level telecommunication service systems. We assume that a service system can be modelled either by a classic Mt/Mt/S queue, or Mt/Mt/S queue with batch service or Mt/Mt/S with catastrophes and batch arrivals when empty. The question under consideration is: how many servers guarantee that in the long ru...

We consider a two-node fluid network with batch arrivals of random size having a heavy-tailed distribution. We are interested in the tail asymptotics for the stationary distribution of a two-dimensional queue-length process. The tail asymptotics have been well studied for two-dimensional reflecting processes where jumps have either a bounded or an unbounded light-tailed distribution. However, p...

We consider a batch arrival queueing system with two phases of service, feedback and K optional vacations under a classical retrial policy. At the arrival epoch, if the server is busy the whole batch joins the orbit. Whereas if the server is free, then one of the arriving customer starts its service immediately and the rest joins the orbit. For each customer, the server provides two phases of s...

This paper treats a discrete-time batch arrival queue with single working vacation. The main purpose of this paper is to present a performance analysis of this system by using the supplementary variable technique. For this purpose, we first analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. Next, we present the stationary distributions of the system len...