An asymptotic analysis of a queueing system with Markov-modulated arrivals
Operations Research
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Analysis of an Infinite-Server Queue with Batch Markovian Arrival Streams
Queueing Systems: Theory and Applications
MRMSolve: Distribution Estimation of Large Markov Reward Models
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
The Pht/Pht/8 Queueing System: Part I--The Single Node
INFORMS Journal on Computing
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This paper investigates a queuing system with infinite number of servers where the arrival process is given by a Markov Arrival Process (MAP) and the service time follows a Phase-type (PH) distribution. They were chosen since they are simple enough to describe the model by exact methods. Moreover, highly correlated arrival processes and heavy-tailed service time distributions can be approximated by these tools on a wide range of time-scales. The transient behaviour of the system is analysed and the time-dependent moments of the queue length is computed explicitly by solving a set of differential equations. The results can be applied to models where performance of parallel processing is important. The applicability of the model is illustrated by dimensioning a WEB-based content provider.