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In queueing theory, a discipline within the mathematical theory of probability, a Markovian arrival process (MAP or MArP [1]) is a mathematical model for the time between job arrivals to a system. The simplest such process is a Poisson process where the time between each arrival is exponentially distributed. [2] [3]
A M/M/1 queue means that the time between arrivals is Markovian (M), i.e. the inter-arrival time follows an exponential distribution of parameter λ. The second M means that the service time is Markovian: it follows an exponential distribution of parameter μ. The last parameter is the number of service channel which one (1).
The system is described in Kendall's notation where the G denotes a general distribution for both interarrival times and service times and the 1 that the model has a single server. [3] [4] Different interarrival and service times are considered to be independent, and sometimes the model is denoted GI/GI/1 to emphasise this.
Time value of money problems involve the net value of cash flows at different points in time. In a typical case, the variables might be: a balance (the real or nominal value of a debt or a financial asset in terms of monetary units), a periodic rate of interest, the number of periods, and a series of cash flows. (In the case of a debt, cas
The time value of money means that money is worth more now than in the future because of its potential growth and earning power over time. In other words, receiving a dollar today is more valuable ...
The arrivals in the process whose intensity is () are the "daughters" of the arrival at time . The integral ∫ 0 ∞ ϕ ( t ) d t {\displaystyle \int _{0}^{\infty }\phi (t)\,dt} is the average number of daughters of each arrival and is called the branching ratio .
Time to value (TTV) is a measure of the length of time necessary to undertake a project and realize the benefits of the solution. The concept is used to help decision makers evaluate the proposed benefit of an investment in time and/or money. [ 1 ]
It is an extension of an M/M/1 queue, where this renewal process must specifically be a Poisson process (so that interarrival times have exponential distribution). Models of this type can be solved by considering one of two M/G/1 queue dual systems, one proposed by Ramaswami and one by Bright.