## LINE

**LINE:**an open-source solver for queueing network models based on ordinary differential equations. Binaries, source and documentation available from the

**LINE website**.

LINE can be integrated with the Palladio Bench suite for the QoS analysis of software applications. LINE is based on the concept of mean-field theory, in which the interactions among a large population of entities are approximated by a single averaged effect.

More details on this tool can be found on the following papers:

**LINE: Evaluating Software Applications in Unreliable Environments.**

J.F. Pérez and G. Casale.

Accepted in IEEE Transactions on Reliability. [DOI]

**Assessing SLA compliance from Palladio component models**

J. F. Pérez and G. Casale. Proceedings of the 2nd Workshop on Management of resources and services in Cloud and Sky computing (MICAS), 2013.

## jMarkov/jPhase

**jMarkov**and

**jPhase:**object-oriented tools for modeling and so`lving large-scale Markov Chains and represent Phase-Type distributions. Visit the

**jMarkov website at COIN-OR**.

This tool facilitates the development of large-scale Markov chains. It is composed of four modules: jMarkov (to build and analyze Markov chains); jQBD (for Quasi-Birth-and-Death processes); jPhase (to represent Phase-Type distributions); and jMDP (for Markovian Decision Processes).

More details on these tools can be found on the papers:

**Algorithm 972: JMarkov: An Integrated Framework for Markov Chain Modeling.**

J.F. Pérez, D.F. Silva, J.C. Góez, A. Sarmiento, A. Sarmiento-Romero, R. Akhavan-Tabatabaei and G. Riaño.

ACM Transactions on Mathematical Software, Vol. 43, No. 3, 2017. [DOI]

**jMarkov: An Object Oriented Framework for Modeling and Analyzing Markov Chains and QBDs**,

G. Riaño and J. Góez. Proceedings of the SMCtools’06, October 2006.

**jPhase: an object- oriented tool for modeling Phase-Type distributions.**[PDF]

J.F. Pérez and G. Riaño. Proceedings of the SMCtools’06, October 2006.

## Q-MAM

**Q-MAM:**A MATLAB toolbox for solving

*Infinite Queues*using Matrix Analytic Methods (Visit the website). This tool requires the SMCSolver tools, which can be found here.

This tool is composed of a set of MATLAB functions (i.e., .m files) to compute the queue length, waiting time and delay distributions of various queueing systems of infinite size. It includes, among others, implementations of the following queueing models, both in discrete and continuous time: PH/PH/1, MAP/MAP/1, MAP/M/c, MAP/D/c, RAP/RAP/1, MMAP[K]/PH[K]/1, MMAP[K]/SM[K]/1, SM[K]/PH[K]/1. State-of-the-art solution techniques are used to solve these models efficiently.

More details on this tool can be found on the paper:

*Q-MAM: A Tool for Solving Infinite Queues using Matrix-Analytic Methods*,

J.F. Pérez, J. Van Velthoven and B. Van Houdt.