A batch-service queueing model with a discrete batch Markovian arrival process

Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model

Tail distribution of the delay in a general batch-service queueing model

A

Determining milk isolated and conjugated trans-unsaturated fatty acids using Fourier transform Raman spectroscopy

The feasibility of Raman spectroscopy in combination with partial least-squares (PLS) regression for the determination of individual or grouped trans-monounsaturated fatty acids (trans-MUFA) and conjugated linoleic acids (CLA) in milk fat is demonstrated using spectra obtained at two temperature conditions: room, temperature and after freezing at -80 degrees C. The PLS results displayed capability for direct semiroutine quantification of several individual CLA (cis-9,trans-11 and trans-10,cis-12 C18:2) and trans-MUFA (trans-4-15 C18:1) in minor concentrations (below 1.0 g/100 g of milk fat). Calibration models were based on reference data cross-correlation or determined by specific scattering signals in the Raman spectra. Distinct bands for trans-MUFA (1674 cm(-1)) and CLA (1653 cm(-1)) from the trans isolated and cis,trans conjugated C=C bonds were identified, as well as original evidence for the temperature effect (new bands, peak shifts, and higher intensities) on the Raman spectra of fatty acid methyl ester and triacylglyceride standards, are supplied

Complete characterisation of the customer delay in a queueing system with batch arrivals and batch service

Whereas the buffer content of batch-service queueing systems has been studied extensively, the customer delay has only occasionally been studied. The few papers concerning the customer delay share the common feature that only the moments are calculated explicitly. In addition, none of these surveys consider models including the combination of batch arrivals and a server operating under the full-batch service policy (the server waits to initiate service until he can serve at full capacity). In this paper, we aim for a complete characterisation-i.e., moments and tail probabilities - of the customer delay in a discrete-time queueing system with batch arrivals and a batch server adopting the full-batch service policy. In addition, we demonstrate that the distribution of the number of customer arrivals in an arbitrary slot has a significant impact on the moments and the tail probabilities of the customer delay

The Discrete-Time Bulk-Service Geo/Geo/1

This paper deals with a discrete-time bulk-service Geo/Geo/1 queueing system with infinite buffer space and multiple working vacations. Considering an early arrival system, as soon as the server empties the system in a regular busy period, he leaves the system and takes a working vacation for a random duration at time n. The service times both in a working vacation and in a busy period and the vacation times are assumed to be geometrically distributed. By using embedded Markov chain approach and difference operator method, queue length of the whole system at random slots and the waiting time for an arriving customer are obtained. The queue length distributions of the outside observer’s observation epoch are investigated. Numerical experiment is performed to validate the analytical results