Transient analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions

This paper introduces an efficient numerical algorithm for transient analysis of deterministic and stochastic Petri nets (DSPNs) and other discrete-event stochastic systems with exponential and deterministic events. The proposed approach is based on the analysis of a general state space Markov chain (GSSMC) whose state equations constitute a system of multidimensional Fredholm integral equations. Key contributions of this paper constitute the observations that the transition kernel of this system of Fredholm equations is piece-wise continuous and separable. Due to the exploitation of these properties, the GSSMC approach shows great promise for being effectively applicable for the transient analysis of large DSPNs with concurrent deterministic transitions. Moreover, for DSPNs without concurrent deterministic transitions the proposed GSSMC approach requires three orders of magnitude less computational effort than the previously known approach based on the method of supplementary variables

A Unified Approach for Improving QoS and Provider Revenue in 3G Mobile Networks

In this paper, we introduce a unified approach for the adaptive control of 3G mobile networks in order to improve both quality of service (QoS) for mobile subscribers and to increase revenue for service providers. The introduced approach constantly monitors QoS measures as packet loss probability and the current number of active mobile users during operation of the network. Based on the values of the QoS measures just observed, the system parameters of the admission controller and packet scheduler are controlled by the adaptive performance management entity. Considering UMTS, we present performance curves showing that handover failure probability is improved by more than one order of magnitude. Moreover, the packet loss probability can be effectively regulated to a predefined level and provider revenue is significantly increased for all pricing policies

Transient analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions

This paper introduces an efficient numerical algorithm for transient analysis of deterministic and stochastic Petri nets (DSPNs) and other discrete-event stochastic systems with exponential and deterministic events. The proposed approach is based on the analysis of a general state space Markov chain (GSSMC) whose state equations constitute a system of multidimensional Fredholm integral equations. Key contributions of this paper constitute the observations that the transition kernel of this system of Fredholm equations is piece-wise continuous and separable. Due to the exploitation of these properties, the GSSMC approach shows great promise for being effectively applicable for the transient analysis of large DSPNs with concurrent deterministic transitions. Moreover, for DSPNs without concurrent deterministic transitions the proposed GSSMC approach requires three orders of magnitude less computational effort than the previously known approach based on the method of supplementary variables

Performance analysis of the general packet radio service

This paper presents an efficient and accurate analytical model for the radio interface of the general packet radio service (GPRS) in a GSM network. The model is utilized for investigating how many packet data channels should be allocated for GPRS under a given amount of traffic in order to guarantee appropriate quality of service. The presented model constitutes a continuous-time Markov chain. The Markov model represents the sharing of radio channels by circuit switched GSM connections and packet switched GPRS sessions under a dynamic channel allocation scheme. In contrast to previous work, the Markov model explicitly represents the mobility of users by taking into account arrivals of new GSM and GPRS users as well as handovers from neighboring cells. Furthermore, we take into account TCP flow control for the GPRS data packets. To validate the simplifications necessary for making the Markov model amenable to numerical solution, we provide a comparison of the results of the Markov model with a detailed simulator on the network level

Transient analysis of deterministic and stochastic Petri nets with concurrent deterministic transitions

This paper introduces an efficient numerical algorithm for transient analysis of deterministic and stochastic Petri nets (DSPNs) and other discrete-event stochastic systems with exponential and deterministic events. The proposed approach is based on the analysis of a general state space Markov chain (GSSMC) whose state equations constitute a system of multidimensional Fredholm integral equations. Key contributions of this paper constitute the observations that the transition kernel of this system of Fredholm equations is piece-wise continuous and separable. Due to the exploitation of these properties, the GSSMC approach shows great promise for being effectively applicable for the transient analysis of large DSPNs with concurrent deterministic transitions. Moreover, for DSPNs without concurrent deterministic transitions the proposed GSSMC approach requires three orders of magnitude less computational effort than the previously known approach based on the method of supplementary variables

Numerical Analysis of Generalized Semi-Markov Processes

This paper present methodological results that allow the cost-effective numerical analysis of finite-state generalized semi-Markov processes (GSMPs) with exponential and deterministic events by an embedded general state space Markov chain (GSSMC). Key contributions constitute the formal proof that elements of the transition kernel of the GSSMC can always be computed by appropriate summation of transient state probabilities of continuous-time Markov chains and the derivation of conditions under which kernel elements are constant. Furthermore, we derive conditions on the building blocks of the GSMP for which state probabilities πi1a1, a26 are symmetric in respect to clock readings of deterministic events concurrently active. The exploitation of these properties is the key driver to the cost-effective time-dependent and stationary analysis of the considered class of GSMPs. The techniques of this paper are applicable to networks of queues, stochastic Petri nets, time-enhanced state charts and UML specifications, and other discrete-event stochastic systems with an underlying stochastic process that can be represented as a GSMP with exponential and deterministic events

Adaptive Call Admission Control for QoS/Revenue Optimization in CDMA Cellular Networks

In this paper, we show how online management of both quality of service (QoS) and provider revenue can be performed in CDMA cellular networks by adaptive control of system parameters to changing traffic conditions. The key contribution is the introduction of a novel call admission control and bandwidth degradation scheme for real-time traffic as well as the development of a Markov model for the admission controller. This Markov model incorporates important features of 3G cellular networks, such as CDMA intra- and inter-cell interference, different call priorities and soft handover. From the results of the Markov model the threshold for maximal call degradation is periodically adjusted according to the currently measured traffic in the radio access network. As a consequence, QoS and revenue measures can be optimized with respect to a predefined goal. To illustrate the effectiveness of the proposed QoS/revenue management approach, we present quantitative results for the Markov model and a comprehensive simulation study considering a half-day window of a daily usage pattern