PASTA Theorem

Poisson Arrivals See Time Average (PASTA)

* Valid for M/*/*
* The the probability that an arriving user sees the system in state i, is equivalent to the average time spent in that state

Review of Telatar "Combining Queueing Theory with Information Theory for Multiaccess"

Paper.


To Do:

* Summarize.
* Check the citing papers. They are of multiple.

Summary of De Veciana and Zemilanov's Work

Papers
1- Main conference paper.
2- Book Chapter describing the derivations.

Scenario:

* A WAN operator who aims to give universal coverage.
* A WLAN operator who aims to give local high performance coverage.
* Users deciding independently.

Modeling:

* Stochastic geometry is used to model both the position of WAN an WLAN AP's, and users.
* The users make greedy decisions maximizing a given utility function.
* Utility functions are either proximity based or capacity based.
* Proximity based changes with the distance.
* Capacity takes into account the delay of an file download assuming Processor Sharing discipline is used at the base station. The delay is modeled as the delay of a M/G/1-Processor Sharing queue. The more number of users, larger the delay.

Results

* The utility function that include both proximity and capacity reaches a global equilibrium.
* The performance metrics are the average delay over the entire user population, and average worst case delay averaged on different WAN service zones. The congestion sensitive mechanisms give %300-%600 increase over the proximity only metrics.
* Furthermore, the congestion sensitive utility functions reduce the spatial load fluctuations, and are able to reduce the back-haul bandwidth required for the WLAN's this is the largest expenditure for these type of access networks.

Notes

* The congestion sensitive utility function, based on the M/G/1/PS is taken from Sem Borst's paper. Borst in turn takes this from Telatars 1995 paper.