×

Markov-additive processes of arrivals. (English) Zbl 0845.60090

Dshalalow, Jewgeni H. (ed.), Advances in queueing. Theory, methods, and open problems. Boca Raton, FL: CRC Press. Probability and Stochastics Series. 167-194 (1995).
Summary: A Markov-additive process (MAP) of arrivals is a process \(({\mathbf X}, J)\) on the state space \(\mathbb{N}^r \times E\) such that the increments in \(\mathbf X\) correspond to arrivals. A typical example is that of different classes of arrivals at a queueing system. We investigate the lack of memory property, interarrival times and moments of the number of counts. We then consider transformations of the process that preserve the Markov-additive property, such as linear transformations, patching of independent processes, and linear combinations. Random time transformations are also investigated. Finally, we consider secondary recordings that generate new arrival processes from the original process. These include, in particular, marking, coloring, and thinning. For Markov-Bernoulli recording, the secondary process, in each case, turns out to be a MAP of arrivals.
For the entire collection see [Zbl 0836.00013].

MSC:

60K15 Markov renewal processes, semi-Markov processes
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
60K25 Queueing theory (aspects of probability theory)
PDFBibTeX XMLCite