Erlang formula

If an electrode surface is considered to contain a multiple set of identically functioning single active centres/servers, where each ion can have a choice of several adjacent servers,28 the probability that exactly j number of severs is occupied at any given time may be computed by the Erlang formula (Eq. 15), provided that numerical values of X and //, or r = XI/a are known. From a practical point of view, two particular states are of interest s0, where the entire surface is free for an electrode reaction to proceed, and, vm, where the entire surface is covered by the reaction product m is the number of active centres, or clusters of active centres. A small value of r represents either a slow arrival of ions, or a fast electrode reaction, and vice versa. When r = 1, the arrival and surface rates are matched exactly. Table 6 shows the effect of r on (i) the probability of the entire electrode surface... 

Probabilities Predicted by the Erlang Formula for a Completely Free, and a Completely Occupied Surface at Various Surface Efficiencies. M = 5... 

Cluster Efficiency by Erlang s Formula Applied to the Oxide Layer Thickness Problem25... 

Because Krogh credited the help of the mathematician Mr. Erlang [118] in deriving this formula, this model is appropriately referred to as the Krogh-Erlang model. 

With n = s, this is the proportion of time that ail s circuits are busy. This is also the proportion of arriving calls that are lost, because of the PASTA property to be discussed below in Section 5.5. Equation (42) in the case n = i is the celebrated Erlang loss formula. 

This also was known as Erlang C formula. The equation could be expressed by C (X, fi, n) (Koole and Mandelbaum 2001). Noted the incoming calls randomly arrived at a constant rate X, service process also follows an exponential distribution with fixed rate // and operated by staffing level n (Aktekin 2014). 

According to the assumptions of the call center operations, it was limited to the M/M/n model. The feasible number of required agents was determined by Erlang C formula subject to the expected service level at least or equal to 80 % with waiting time less than 20 s. The main inputs were arrival rate and service rate in every single hour over 13-working period entire the month. To determine arrival rate in period ijk, the hourly call arrivals were divided by 3600 s that equal to calls per second. In addition to the arrival rate,. ijk calls per second in period ijk was the fraction of AHT in the same period. Let j = 1,2, 3. .. 13 represented to period 1-13, f = 1, 2, 3. .., 7 marked from Sunday to Saturday, and k=, 2,3 and 4 started from Week 5 to Week 8. 

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