Input characterization to describe the flow of incoming traffic in network systems, such as the GRID and the WWW, is often performed by using Markov Modulated Poisson Processes (MMPP). Therefore, to enact capacity planning and Quality-of-Service (QoS) oriented design, the model of the servers that receive the incoming traffic is often described as a MMPP/M/1 queue. In a recent work we have provided an approximate solution for the response time distribution of the MMPP/M/1 queue, which is based on a hyper-exponential process obtained via a weighted superposition of the response time distributions of M/M/l queues. Compared to exact solution methods, or simulative techniques, the aim of this approximation is to provide the potential for more efficient model solution, so to enable, e.g., real-time what-if analysis in system reconfiguration scenarios. In this paper, we show how fast the computation can be supported in practical settings by ad-hoc techniques allowing the hyper-exponential model to be solved with no iterative or numerical costly steps, which would otherwise be required in order to compute the length of transient phases due to state switches in the MMPP arrival process. An application to the context of performance analysis of a GRID system is also shown, supporting the efficiency of our proposal. © 2008 IEEE.
Fast computation of hyper-exponential approximations of the response time distribution of MMPP/M/1 queues / Romano, Paolo; Ciciani, Bruno; Andrea, Santoro; Quaglia, Francesco. - (2008), pp. 113-120. (Intervento presentato al convegno 41st Annual Simulation Symposuim, ANSS 2008 tenutosi a Ottawa; Canada nel 13 April 2008 through 16 April 2008) [10.1109/anss-41.2008.28].
Fast computation of hyper-exponential approximations of the response time distribution of MMPP/M/1 queues
ROMANO, Paolo;CICIANI, Bruno;QUAGLIA, Francesco
2008
Abstract
Input characterization to describe the flow of incoming traffic in network systems, such as the GRID and the WWW, is often performed by using Markov Modulated Poisson Processes (MMPP). Therefore, to enact capacity planning and Quality-of-Service (QoS) oriented design, the model of the servers that receive the incoming traffic is often described as a MMPP/M/1 queue. In a recent work we have provided an approximate solution for the response time distribution of the MMPP/M/1 queue, which is based on a hyper-exponential process obtained via a weighted superposition of the response time distributions of M/M/l queues. Compared to exact solution methods, or simulative techniques, the aim of this approximation is to provide the potential for more efficient model solution, so to enable, e.g., real-time what-if analysis in system reconfiguration scenarios. In this paper, we show how fast the computation can be supported in practical settings by ad-hoc techniques allowing the hyper-exponential model to be solved with no iterative or numerical costly steps, which would otherwise be required in order to compute the length of transient phases due to state switches in the MMPP arrival process. An application to the context of performance analysis of a GRID system is also shown, supporting the efficiency of our proposal. © 2008 IEEE.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.