What is the High loss calculation?
What is the high loss and how can it be calculated (High loss calculation)?
High loss systems is a common phenomenon in many telecommunications systems and therefore the knowledge of what it is, how it can be determined, and how it can be alleviated is of importance to any telecommunications service provider. This discussion is aimed at providing an understanding the high-loss system and its calculation. Emphasis has been made to generalize the theory based on a switching system that suffers a high loss situation generated by a ‘peculiar’ but common subscriber calling phenomenon. Traditional erlang lost calculations do not take into considerations the abnormal behavior that occurs in high loss systems and therefore an alternative approach must be sought.
High loss system 
A high loss system is characterized by a considerable increase in offered traffic above the system capacity and resultant congestion which may result to overload. This is a phenomenon that occurs when callers reattempt calls when faced with congestion. Congestion leads to further congestion . The offered traffic ceases to follow a poissonian arrival process and becomes a function of blocking. This avalanche like effect leads to an overload which may in turn go to the extent of bringing down the system leading to zero carried traffic. As this happens, the size of offered traffic continues to grow immensely.
Consider an example when a telecommunications service company announces a very attractive tariff promotion that has a stated time of offer. Subscribers will want to take advantage of the promotion and if the company did not anticipate the increase in traffic or considered classical methods in forecasting traffic, will suffer congestion. Circuits will all get occupied and subscribers encountering blocked calls will redial one or more times. Many events that can lead a switching system going to a high-loss situation such as:
· Failure of a load sharing component/s leading to reduced capacity under normal traffic conditions.
· Failure of a link or a switching system leading to callers attempting to call their intended calls at about the same time.
· Unplanned introduction of a service that attracts a sudden or upswing demand.
Users may affect the system in two kinds of behavior: Impatience and reattempts .
Impatience can be placed in two kinds which are: premature dialing and premature hanging up.
Premature dialing 
Premature dialing comes in to play when the traffic load is high an the normal call setup times are not as fast. For instance, when a caller has been used to an instant dial tone goes off-hook and start dialing before the dial tone arrives, he is unaware that the digits recognized are from when the dial tone arrived. The switch will get only part of the digits dialed. The subscriber will interpret this as a failed attempt and redial, but the switch has circuits and processor resources occupied.
Premature hang-up 
The subscriber may go on-hook while his call is still being processed. But because of impatience hangs up. Use of tones to signal the user that connection is in progress can help to clear such a situation .
Erlang traffic calculations make assumptions about call arrival process which only apply in a balanced traffic scenario and where the user has patience. They assume that a queuing model where the caller has indefinite patience. They assume that the calls follow a poisonnian distribution process and calls encountering congestion exit from the system. They do not sufficiently take into consideration the abnormal process introduced about a high-loss system. In a high loss system, offered traffic is no longer a function of poissonian demand but a function of blocking.
A brief definition of terminology used in reattempts is necessary to understanding the analysis of a high loss system. Below are the main significant ones :
Call demand: This is an intention or desire to make a call and results in a call attempt.
Call attempt: The operation of attempting to make a connection to the intended party in a communication.
Fresh call: The initial or first call attempt. Any other call attempt after this is a reattempt.
Coefficient of call repetition β: The average number of repeated calls after the call intention.
Efficiency rate r: a ratio of the number of successful call attempts to the number of call attempts.
Rank of reattempt n: The subsequent number of the reattempt after the first attempt.
Analysis of reattempts 
The theory of reattempts can be assessed in a global model which analyses the quality and composition of offered traffic as determined by failure probability and subscriber behavior. Below is an illustration of a traffic system with reattempts (Adapted from  p205)
Where λc is the carried traffic that results in a successful connection, p is the probability of call rejection, R is the probability of caller resilience or perseverance, λo is the fresh traffic that is offered to the system. λ1 is the total traffic taken by the system which is a sum of fresh offered traffic and reattempted traffic. We can derive a relationship of a general model between the efficiency rate r, the probability of call rejection p and the call repetition coefficient β. From the diagram above we can deduce that
‘λc =λ1(1-p)’………………………………………………………......... (1)
λ1 = λo + Rp λ1 …………………………………..………….….…..… (2)
λ1 = λo / (1-Rp) = β λo…………………………....….....…...............(3)
Hence β = 1/ [1-R (1-r)]………………….………..............…………. (4)
We need to determine the probability of failure of a call reattempt in the nth rank of attempt. Let us consider a switching system which has m outgoing directions (trunk groups) with failure rates of fi , i=1, 2, 3,……..,m. let λoi be the fresh offered traffic towards a direction i.
The rate of failure in the first attempt can be determined as:
The general rate of failure at a reattempt of rank k can be given as:
Since the probability of arrival of the first call attempt can be described as a following poissonian distribution and the failure of the first attempt as following a blocking probability derived from Erlang B calculations, more specific derivation for the probability of a call reattempt failure can be modeled (209) as below where F (t) is a function representing time distribution between call attempts.
Overload condition. 
When the utilization of traffic handling and processing resources such as processors, memories, circuit and trunks goes beyond nominal, an overload condition presents itself. Different operators set different nominal values to indicate the level of overload such as 70% or 80%. At these levels the traffic engineers are alerted of an impeding overload. They may then take appropriate action such as increasing signaling capabilities, adding more circuits, defining and creating alternative routes, or control incoming traffic. A situation occurs when an actual overload occurs on the system which is above the user defined threshold. The offered traffic grows immensely
If the maximum processing load the processor can handle is φmax to carry a maximum traffic of λmax then φmax must be less than 1 to allow for the background tasks of the processor which cannot be delayed indefinitely. If the amount of traffic offered exceeds λmax and overload occurs and the calls have to be queued beyond a subscriber’s patience. The subscriber will reattempt the call and lead to further congestion. This cyclic process will lead to a breakdown of the system and carried traffic will be zero while the offered traffic continues to grow indefinitely the graph below [adapted from  215].
The unpleasant consequence of overload is that is takes a long time before its effect clears and returns to a state of equilibrium.
Overload control. 
A brief mention of methods that can be applied to control overload is important to know how to deal with overload and guarantee an acceptable level of service to users. Two methods can be applied. The first is regulation in centralized systems and the second one regulation in distributed systems .
Regulation in centralized systems 
This operates in the principle of passive filtering of incoming calls in a last in first out basis (LIFO). This ensures that impatient customers who renew calls every time they fail to get connection are rejected by the system. The subscribers are placed in a queue contained in a buffer of limited size. Patient customers have a higher likelihood of getting a connection. If they do not dial prematurely, they are placed in a queue to wait for the processor to be free. The digits are evaluated from the last digit to avoid callers who go on-hook mid-dial or dial prematurely .
Regulation in distributed systems 
In a distributed system, the task of detecting and handling calls and overloads is delegated to other distributed processors. Congestion control is done by distributed systems such as subscriber line interface peripherals. Since these elements handle less traffic, their probability of failure is low. The output of such systems is dimensioned to be such that the total load from all distributed systems cannot overload the central processor. This system adopts the last in first served approach where recent calls have the least probability of failing .
In the foregoing discussion, we have described the high-loss system, its causes, effects, determination of its descriptive parameters and also two methods applied in alleviation the effects of an overload system. Also brought out is the limitation of erlang equations in predicting circuit requirements in for re-entrant traffic . This is not an exhaustive analysis but an integration of the main aspects of a high-loss system. The control of overload requires an independent detailed analysis that could not be done here and further reading is recommended.
Further reading suggestions 
1. Songhurst D. Subscriber Repeat Attempts, Congestion, and Quality of Service: A Study Based On Network Simulation. Proceedings of the 10th international teletraffic congress, Montréal, 1983, paper 5-2-4.
2. Forys L., Performance Analysis Of A New Overload Strategy. Proceedings of the 10th international teletraffic congress, Montréal, 1983, paper 1-1-5.
1. What is a high loss system?
2. What are the limitations of erlang loss calculations as far as a high loss systems concerned?
3. define the following terms:
a) Call demand
b) Call attempt
c) Rank of reattempt
d) Efficiency rate
e) Coefficient of repetition.
4. A telecommunication system has carried traffic load of 0.583 erl. Find the total traffic including reattempt traffic. Determine also the blocked traffic if the probability call rejection is 0.36?
Kennedy I., School of Electrical and Information Engineering, University of the Witwatersrand, a Personal Communication.
Hebuterne G., Traffic Flow in Switching Systems, Artec house Inc, Norwood MA, 1987