Though well established from a technical standpoint, wireless telephony still faces numerous obstacles on its path to a ubiquitous, satisfying user experience. Still, the best way to acquire more subscribers and keep them satisfied is to make the service as easy to use and as reliable as possible. Wireless companies should strive to become equal with land-based connections in terms of voice quality, pervasiveness of connections, and value-added services.
Unfortunately, this level of service isn't so easy to achieve. At the core of the problem is the fact that wireless basestations can only handle a finite number of calls. Until they ramp up in capacity, there will always be situations where users cannot make a connection. If these users are mobile, any connections that are established can be easily dropped during handoff.
These problems are only exacerbated by challenges such as public gatherings, sporting and concert events, traffic congestion, and the notoriously unpredictable, accident-related basestation overloads. To alleviate these difficulties, the art of traffic engineering has taken center stage in the drive to improve the user experience.
Traffic engineering is key to effective wireless telephony network design and planning. In the process, traffic characteristics need to be addressed. Once accomplished, mathematical models can be applied to the dimensioning of the network. Dimensioning determines the amount of traffic the radio equipment captures. An accurate traffic model for the system greatly enhances the accuracy of network dimensioning, extending network investments and increasing the profit returns. Because the equipment is used more efficiently, it can capture the majority of the traffic and produce greater user satisfaction.
On the flip side, poor modeling of traffic characteristics can actually affect system performance. When cells are under-dimensioned, not enough radio channels are installed. This congests the cell, and it also may affect overall system performance.
Before approaching the problem of network dimensioning, it's essential to understand the Erlang-B formula, which forms the basis of the required mathematical models. Once understood, the formula can be used to model the various real-life scenarios, providing accurate dimensioning of any given network.
Traffic is defined as the use of given resources. Traffic on a highway is the number of cars that use the highway for transportation. Increased traffic on the highway implies that it is used more1. Bank traffic involves the use of tellers. Greater traffic on the system implies a better use of tellers. In wireless telephony networks, traffic is defined as the use of radio channels.
Revenue from a wireless network is directly proportional to the amount of time that communication channels are being occupied. When a user makes a phone call, a channel is seized for communications, generating traffic. As a result, traffic is proportional to the average call duration.
Traffic is related to the use of radio channels. Traffic value is directly proportional to the frequency of phone calls and the average duration of those calls. Traffic per subscriber (ρ′) in a wireless network is defined as
ρ′ = λ′ × 1/µ Erlang
where λ′ is the number of calls a user makes in a given period, and 1/µ is the average duration of each call. The unit is the Erlang2. The equation can be interpreted as how long on average a user occupies a radio channel, within a certain amount of time. In traffic-engineering terminology, traffic per subscriber is often called traffic intensity. If a user in a wireless system makes an average of two phone calls an hour, with each call lasting 1.5 min., the traffic per subscriber (ρ′) would be
ρ′ = 2/60 × 1.5 = 50 mE
Users in a telephony network on average would call n times an hour. Each call would last for m seconds. Traffic intensity, or traffic per subscriber (ρ′), would therefore be
ρ′ = (n × m)/3600 E (1)
A wireless network can be generally modeled as a queuing system. A queuing system has customers, servers, and waiting rooms. Its characteristics are governed by the arrival behavior and serving behavior. Arrival behavior is the probability distribution of customer arrivals—that is, how often a customer would arrive at the system. Serving behavior is the probability distribution of service. Upon arrival, customers will spend time being served. The distribution of the serving time is the serving behavior. In queuing theory, different models are based on different queuing scenarios. The simplest one takes the form M/M/1/×.
The first M, which represents the arrival distribution, is memoryless3. The arrival of one customer is independent of other customers. This is generally true for any wireless communication system. The second M, representing the serving distribution, also is memoryless. The serving time of a customer is independent of all other customers. The 1 means there is only one server in a system, while the × indicates that there is an infinite number of waiting rooms in the queuing system4. The probability of this system having k customers (Pk) is defined as
Pk = (1 − ρ)ρk
where ρ = λ/µ′ is the total arrival rate, and 1/µ is the mean serving time.[1]
Engineers using this model make four assumptions. Primarily, the population of customers is infinite. That is, there is an unlimited supply of customers. Next, a served customer leaving the system would not immediately return. Third, all customers waiting in the line cannot leave the system. Finally, the system would be first-come, first-served.
A similar model can be applied to wireless telephony systems. Servers are radio traffic channels in each cell. Customers are calls from different mobiles. In queuing theory's terminology, a cell with n radio traffic channels can be described by M/M/n/n. Erlang studied this system and devised some very useful formulas during the 1910s. His research lead to the Erlang-B formula, which is the most widely used formula for traffic engineering.
The queuing model of an M/M/n/n system can be represented by Figure 1. In the diagram, λ is the total arrival rate, which is different than that defined in traffic intensity. It also is defined as the rate at which customers from a group of customers arrive at a system. Meanwhile, n is the number of servers in the system. Each customer will be served at the rate of µ, meaning each customer will finish service in 1/µ unit of time. Distributions of customer arrivals and service times are assumed to be memoryless. There is no waiting room at the system. When all n servers are busy, customers are lost. When a customer has finished service, it leaves the system forever and doesn't return to the system for additional service.
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