A skill based parallel service system under FCFS-ALIS — steady state, overloads, and abandonments

Design and evaluation of overloaded service systems with skill based routing, under FCFS policies

“…(iv) There will be complete resource pooling as in (1) in each of the sub-systems C (l) , S (l) , and the matching rates between customers and servers will be given by (2), with α i and β j replaced by α (l) i and β (l) j , and the following relation will hold:…”

“…Continuing with the remaining customer and server types, the unique decomposition, will emerge as in [2]. The values of the matching rates, in each of the sub-systems of the decomposition, are then given by (2).…”

“…Continuing with the remaining customer and server types, the unique decomposition, will emerge as in [2]. The values of the matching rates, in each of the sub-systems of the decomposition, are then given by (2). Expression (6) for n j simply equates the amount of work done per time unit (assuming that servers are always busy) and the expected amount of work offered per time unit by the fraction r i j of the customers that are served over all c i ∈ C(s j ).…”

“…For each subsystem, we choose appropriate values β (l) j resulting in complete resource pooling: β (1) = (0.5, 0.5) and β (2) = (1). Note that β 1 = β 3 = 0.5 × α 2 = 0.232 and β 2 = α 1 + α 3 = 0.537.…”

“…Our algorithm is based on recent results in [1,2], and on some assumptions on the asymptotic behavior of the system under many server scaling. Our main assumption is that, under many server scaling, the sequence of types are i.i.d.…”