 Hello everyone, welcome to a video lecture on Trunking and Grade of Service. I am K. R. Biradhar, Assistant Professor, Department of Electronics and Telecommunication Engineering, Walsh and the Institute of Technology, Salapur. Let us start with the learning outcomes first. At the end of this video, you will be able to explain Trunking theory in cellular system. Introduction to begin with definition of Trunking system. Cellular radio systems rely on Trunking to accommodate a large number of users in a limited radio spectrum. Trunking system, a mechanism to allow many user to share fewer number of channels. In other words, Trunking theory allows a large number of users to share the relatively small number of channels in a cell by providing access to each user on demand from a pool of available channels. By assuming not every user calls at the same time. If the system has number of call requests which are greater than available channels that causes finality that is blocking effect. If traffic is too heavy call is blocked. Small blocking probability is desired the system to be efficient a small blocking probability is required so that customers will be satisfied. There is a tradeoff between the number of available circuits and blocking probability. Definitions of the terms used in Trunking theory. Let us look at some terms and definitions. First of all setup time is defined as the time required to allocate a radio channel to a requesting user please remember there is a finite time that will elapse from the start of the request to you being actually granted the call. In fact, what is normally done is the total users in much larger than the total available channels at any time we believe that not everybody is going to talk at the same time. Based on this faith total numbers are much larger than the available channels however if someone requests one of the available channel is allocated. After the call is over the channel is returned to the channel full blocked call a call which cannot be completed at the time of request due to congestion in literature it sometimes called last call. Last call is the last revenue I would not like to have too many blocked calls in new year time you will find most of the mobile phone are facing the problem of blocked call because too many people are trying to make the call. Holding time average duration of a typical call which is denoted by h in seconds suppose you are lucky and you actually get into conversation you will use the channel for certain duration of time some people talk longer than others there is a notion of average duration of a typical call that is called the holding time. This holding time can be increasing or decreasing the cost per minute so the mobile companies can play around with the holding time by changing the tariff. Today price is going down because of computation, Erlang the amount of traffic intensity carried by a channel that is completely occupied for example a radio channel that is occupied for 30 minutes during an hour carries 0.5 Erlangs of traffic and one hour carries 1 Erlang of traffic. Traffic intensity measure of channel time utilization which is the average channel occupancy measured in Erlangs. This is a dimension less quantity and may be used to measure the time utilization of single or multiple channels and it is denoted by a and is equal to lambda into h where lambda is the number of calls per hour and h is the holding time. Let us see one example of how to find the traffic intensity here given number of calls per hour is equal to 1800 holding time h is equal to 3 minute what is the traffic intensity pass the video and write solution for the problem. I think you might have written the answer let us see the answer the traffic intensity is given by a is equal to lambda into h therefore a is equal to lambda is 1800 into h is a 3 minutes that if you want to convert 3 divided by 60 in seconds which is equal to 90 Erlangs. There are 90 Erlangs of traffic for 1800 calls per hour with a holding time of 3 minutes. Let us continue some more definitions here load traffic intensity across the entire trunked radio system measured in Erlangs. Grade of service grade of service is a measure of the ability of a user to access a trunked system during the busiest hour. A measure of congestion which is specified as the probability it should depend on many things it should depend on user who are trying to make a call and how long hold the call once they get connected. So the two kinds of probabilities that we might be interested first one probability of a call being blocked Erlang be if my service provider has designed his system for higher probability of call or second one the other probability of a call being delayed a certain amount of time which is Erlang see. So behind a certain amount of time the user will always lose a patience and give up a call it is a bad business strategy. So we have two kinds of charts and associated formula one is called Erlang be formula and associated with Erlang be chart and Erlang see formula and associated with Erlang see charts request rate. The average number of call requests per unit time which is denoted by mu typically in an office environment it could be 5 calls per hour from home environment it could be 2 calls per hour in call center 35 calls per hour or even more. So mu change is from place to place computation of GOS in this slide we shall see what is the total traffic intensity offered by the system for a system containing users and an unspecified number of channels total offered traffic intensity a is given by a is equal to u into a u where u is the total users in a system where a u is the each user generate a traffic intensity of a u Erlangs. The traffic intensity offered by each user is equal to the call request rate multiplied by the holding time that is each user generates a traffic intensity of a u Erlangs which is given by a u is equal to lambda into h where lambda is the average number of call requests per unit time for each user h is the average duration of a typical call. Furthermore in a c channel trunked system if the traffic is equally distributed among the channels then the traffic intensity per channel a c is given by a c is equal to u into a u divided by c where c is the number of channels in a trunking system. Trunking and grade of service there are two types of trunked systems block calls cleared system in the first type of system offers no giving for all call request that is for every user who requests service it is assumed that there is no setup time and user is given immediate access to a channel if one is available. If no channels are available the requesting user is blocked without access and is free to try again later. Second one is blocked calls delayed system QB is provided to hold calls which are blocked if a channel is not available immediately the call request may be delayed until a channel becomes available this type of trunking system is called blocked calls delayed system. These are the references I referred to prepare the above presentation. Thank you.