Analysis for Blocking Probabilities.

Model Setup
The system can be approximated using by a Continuous Time Markov Chain.

Let the call incoming rate be RI and average call service time be ST
Assume that there are 2 Gateways: GW1 and GW2. Let the capacities be N1 and N2 repectively.

Let's assume that the last known update had gatew states as I1 and I2. And the gateway selection probabilities for the two gateways be P1 and P2. 


It is obvious that P1 + P2 = 1


This can be modeled as a CTMC being split into two CTMCs with CallIncomingRates as P1*RI and P2*RI respectively. The overall blocking probability can be computed as:
Pb = P1*Pb1 + P2*Pb2
Where Pb1 and Pb2 are the blocking probabilities for the two chains for time T - the Update Interval.


Why is steady state analysis not enough?
The steady state blocking probability for a CTMC is given by ErlangB formula. According to which the blocking probability is independent of intitial state and Update Interval. It depends only on the number of states in the chain Ni and the load Ei = Pi * RI * ST. Hence, no fruitful relationship between T and Pb can be found.

Uniformization
Uniformization is a method for transient state analysis of CTMC. The basics lay in re-conceptualizing a CTMCs by DTMCs. A very simple procedure for modeling this is given in http://www.cse.cuhk.edu.hk/~cslui/CSC5420/transient_beamer.pdf and implemented with minimal calculations [Code mailed to the Guide].

Telephony Gateway REgistration Protocol

A protocol is required to communicate reachability and resource information between LS & GWs. Telephony Gateway Registration Protocol (TGREP) is the IETF proposed standard used by gateways for this.

TGREP is considered supplementary to TRIP and share a a lot of procedures and message formats. Gateway in TGREP is the speaker and is therefore typically in a 'send' mode. LSs in TGREP act as receivers and are typically only in 'receive' mode.

TRIP Architecture

Intra Domain Protocol

• LSs learn about GWs in their domain using this.
  Example: ITAD1 & ITAD3 has LSs that are aware of the LSs in their respective domains.
• ITAD3 might also come to know about GWs in ITAD1 through TRIP if provider policies allow. This might be after aggregation LS in ITAD2.

Flow of Information In TRIP

The TRIP Problem Statement

When an End User on an IP network wants to complete a call to a phone number on the circuit switched network, the call must be routed through a telephony gateway. Selection of such a gateway is a non-trivial process because of the following reasons:

1. Number of candidate gateways can be really large.
2. The gateway owners incur cost when completing calls towards the circuit switched networks. Hence, the users are charged for these services. This may restrict access to the user who have an established relationship with the owner.
3. In many cases gateway owner is not the provider of IP telephony services to users. In such cases the provider policies and its relationships with various Gateway owners determine what gateways to choose.
4. Even the end user policy on what features to use or what provider to use can be taken into consideration.
5. The gateway capacity varies. Load balancing is therefore required for better performance.
6. The gateway capacity varies. Load balancing is therefore required for better performance.
7. Protocols & Feature compatibilities: signalling or media protocols that are being used by the calling party must be available at the gateway. This too determines what gateways can be used.

Hence determining available gateways for completing calls requires directory which cannot be global, but is decided on the basis of inter-provider relationships and other factors. For seamless functioning of this service, therefore, a protocol is required to exchange the gateway routing information. TRIP is one such protocol.

Terminologies

Gateway(GW): The device that connects IP telephony end to the telephony networks.

End User(EU): Ultimate recipient/initiator of calls

Global Switched Telephone Network (GSTN): The worldwide circuit switched network

Location Server (LS): 

• has IP connectivity
• knowledge of GW to terminate calls towards GSTN
• Point of contact for End Users for completing calls
• Responsible for propagation of gateway information

Information Telephony Administrative Domain (ITAD): A set of GWs and LSs under control of a single administrative authority. EUs are customers of an ITAD.

Location Server Policy: Rules governing how LS processes information it sends & receives via TRIP; this includes aggregating, propagating, generation & accepting information.

Telephony Routing Information Base (TRIB): Database of GWs that a location server builds up as a result of participation in TRIP