Erlang-B
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Erlang-B
The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. A single cord circuit has the capacity to be used for 60 minutes in one hour. Full utilization of that capacity, 60 minutes of traffic, constitutes 1 erlang. Carried traffic in erlangs is the average number of concurrent calls measured over a given period (often one hour), while offered traffic is the traffic that would be carried if all call-attempts succeeded. How much offered traffic is carried in practice will depend on what happens to unanswered calls when all servers are busy. The CCITT named the international unit of telephone traffic the erlang in 1946 in honor of Agner Krarup Erlang. In Erlang's analysis of efficient telephone line usage he derived the formulae for two important cases, Erlang-B and Erlang-C, which became foundational results in teletraffic engineeri ...
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High-loss Calculation
The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. A single cord circuit has the capacity to be used for 60 minutes in one hour. Full utilization of that capacity, 60 minutes of traffic, constitutes 1 erlang. Carried traffic in erlangs is the average number of concurrent calls measured over a given period (often one hour), while offered traffic is the traffic that would be carried if all call-attempts succeeded. How much offered traffic is carried in practice will depend on what happens to unanswered calls when all servers are busy. The CCITT named the international unit of telephone traffic the erlang in 1946 in honor of Agner Krarup Erlang. In Erlang's analysis of efficient telephone line usage he derived the formulae for two important cases, Erlang-B and Erlang-C, which became foundational results in teletraffic enginee ...
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Erlang (unit)
The erlang (symbol E) is a dimensionless unit that is used in telephony as a measure of offered load or carried load on service-providing elements such as telephone circuits or telephone switching equipment. A single cord circuit has the capacity to be used for 60 minutes in one hour. Full utilization of that capacity, 60 minutes of traffic, constitutes 1 erlang. Carried traffic in erlangs is the average number of concurrent calls measured over a given period (often one hour), while offered traffic is the traffic that would be carried if all call-attempts succeeded. How much offered traffic is carried in practice will depend on what happens to unanswered calls when all servers are busy. The CCITT named the international unit of telephone traffic the erlang in 1946 in honor of Agner Krarup Erlang. In Erlang's analysis of efficient telephone line usage he derived the formulae for two important cases, Erlang-B and Erlang-C, which became foundational results in teletraffic engineer ...
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Erlang Distribution
The Erlang distribution is a two-parameter family of continuous probability distributions with support x \in independent exponential distribution">exponential variables with mean 1/\lambda each. Equivalently, it is the distribution of the time until the ''k''th event of a Poisson process with a rate of \lambda. The Erlang and Poisson distributions are complementary, in that while the Poisson distribution counts the number of events that occur in a fixed amount of time, the Erlang distribution counts the amount of time until the occurrence of a fixed number of events. When k=1, the distribution simplifies to the exponential distribution. The Erlang distribution is a special case of the gamma distribution wherein the shape of the distribution is discretised. The Erlang distribution was developed by A. K. Erlang to examine the number of telephone calls which might be made at the same time to the operators of the switching stations. This work on telephone traffic engineering has ...
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Grade Of Service
In telecommunication engineering, and in particular teletraffic engineering, the quality of voice service is specified by two measures: the grade of service (GoS) and the quality of service (QoS). Grade of service is the probability of a call in a circuit ''group'' being blocked or delayed for more than a specified interval, expressed as a vulgar fraction or decimal fraction. This is always with reference to the busy hour when the traffic intensity is the greatest. Grade of service may be viewed independently from the perspective of incoming versus outgoing calls, and is not necessarily equal in each direction or between different source-destination pairs. "Grade of Service" sometimes means a measure of inbound call center traffic to verify adherence to conditions to measure the success of customers served. On the other hand, the quality of service which a ''single'' circuit is designed or conditioned to provide, e.g. voice grade or program grade is called the quality of service. ...
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Numerical Stability
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues. On the other hand, in numerical algorithms for differential equations the concern is the growth of round-off errors and/or small fluctuations in initial data which might cause a large deviation of final answer from the exact solution. Some numerical algorithms may damp out the small fluctuations (errors) in the input data; others might magnify such errors. Calculations that can be proven not to magnify approximation errors are called ''numerically stable''. One of the common task ...
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Erlang Programming Language
Erlang ( ) is a general-purpose, concurrent, functional programming language, and a garbage-collected runtime system. The term Erlang is used interchangeably with Erlang/OTP, or Open Telecom Platform (OTP), which consists of the Erlang runtime system, several ready-to-use components (OTP) mainly written in Erlang, and a set of design principles for Erlang programs. The Erlang runtime system is designed for systems with these traits: *Distributed *Fault-tolerant * Soft real-time * Highly available, non-stop applications *Hot swapping, where code can be changed without stopping a system. The Erlang programming language has immutable data, pattern matching, and functional programming. The sequential subset of the Erlang language supports eager evaluation, single assignment, and dynamic typing. A normal Erlang application is built out of hundreds of small Erlang processes. It was originally proprietary software within Ericsson, developed by Joe Armstrong, Robert Virding, an ...
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Discrete-event Simulation
A discrete-event simulation (DES) models the operation of a system as a (discrete) sequence of events in time. Each event occurs at a particular instant in time and marks a change of state in the system. Between consecutive events, no change in the system is assumed to occur; thus the simulation time can directly jump to the occurrence time of the next event, which is called next-event time progression. In addition to next-event time progression, there is also an alternative approach, called incremental time progression, where time is broken up into small time slices and the system state is updated according to the set of events/activities happening in the time slice. Because not every time slice has to be simulated, a next-event time simulation can typically run faster than a corresponding incremental time simulation. Both forms of DES contrast with continuous simulation in which the system state is changed continuously over time on the basis of a set of differential equations d ...
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Call Centre
A call centre ( Commonwealth spelling) or call center (American spelling; see spelling differences) is a managed capability that can be centralised or remote that is used for receiving or transmitting a large volume of enquiries by telephone. An inbound call centre is operated by a company to administer incoming product or service support or information enquiries from consumers. Outbound call centres are usually operated for sales purposes such as telemarketing, for solicitation of charitable or political donations, debt collection, market research, emergency notifications, and urgent/critical needs blood banks. A contact centre is a further extension to call centres telephony based capabilities, administers centralised handling of individual communications, including letters, faxes, live support software, social media, instant message, and email. A call center was previously seen to be an open workspace for call center agents, with workstations that include a computer and d ...
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Spectral Efficiency
Spectral efficiency, spectrum efficiency or bandwidth efficiency refers to the information rate that can be transmitted over a given bandwidth in a specific communication system. It is a measure of how efficiently a limited frequency spectrum is utilized by the physical layer protocol, and sometimes by the medium access control (the channel access protocol).Guowang Miao, Jens Zander, Ki Won Sung, and Ben Slimane, Fundamentals of Mobile Data Networks, Cambridge University Press, , 2016. Link spectral efficiency The link spectral efficiency of a digital communication system is measured in ''bit/ s/ Hz'', or, less frequently but unambiguously, in ''(bit/s)/Hz''. It is the net bit rate (useful information rate excluding error-correcting codes) or maximum throughput divided by the bandwidth in hertz of a communication channel or a data link. Alternatively, the spectral efficiency may be measured in ''bit/symbol'', which is equivalent to ''bits per channel use'' (''bpcu''), implying th ...
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Exponential Distribution
In probability theory and statistics, the exponential distribution is the probability distribution of the time between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includes many other distributions, like the normal, binomial, gamma, and Poisson distributions. Definitions Probability density function The probability density function (pdf) of an exponential distribution is : f(x;\lambda) = \begin \lambda ...
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Call Centre
A call centre ( Commonwealth spelling) or call center (American spelling; see spelling differences) is a managed capability that can be centralised or remote that is used for receiving or transmitting a large volume of enquiries by telephone. An inbound call centre is operated by a company to administer incoming product or service support or information enquiries from consumers. Outbound call centres are usually operated for sales purposes such as telemarketing, for solicitation of charitable or political donations, debt collection, market research, emergency notifications, and urgent/critical needs blood banks. A contact centre is a further extension to call centres telephony based capabilities, administers centralised handling of individual communications, including letters, faxes, live support software, social media, instant message, and email. A call center was previously seen to be an open workspace for call center agents, with workstations that include a computer and d ...
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Iteration
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a co ...
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