Queues with skill based parallel servers and a FCFS infinite matching model

Approximate optimality with bounded regret in dynamic matching models

“…Adan and Weiss [4] have shown that the FCFS (First Come First Served) policy also has a maximal stability region. The stationary distribution under FCFS policy has a product form [2,3], but there is no efficient algorithm for the normalizing constant. The proof of the stability result for ML policy is based on the fact that this policy minimizes the drift of the quadratic Lyapunov function,…”

Design heuristic for parallel many server systems

“…On the other hand, if the system is stable, for small enough λ, under ALIS servers of types S (1) will have shorter idle periods than servers S (2) , who in turn will have shorter idle periods than servers S (3) . Figure 5 shows how such a system will behave under our conjecture.…”

“…Once we determined decomposition level and quality parameters, modifiedα cj can be determined and with pre-specified β sj we then use the bipartite infinite matching model, formula (2), to obtain the matching rates r ci,sj . Once we have the matching rates, we can calculate the amount of work required from each type of server, and this determines, by Little's law, the number of servers that are needed of each type in order to meet the requested quality of service and utilization.…”

“…We use our ability to calculate matching rates in order to design parallel service systems operating under FCFS-ALIS. In [2,1] we presented a heuristic algorithm to determine the required workforce in the Efficiency Driven (ED) overloaded regime. The main contribution of the current paper is to extend this algorithm to other regimes of interest: The Quality Driven (QD) mode in which there is underload, and Quality and Efficiency Driven (QED) mode in which the load is exactly one [21].…”

Balanced fair resource sharing in computer clusters

“…Multi-server queues with specialized servers have already been considered in [8,26,1,25] but these models assume that each job can be processed by only one server at a time. Our model is closer to the multi-server queue with redundant requests introduced by Gardner et al [11,10], where the class of a job defines the set of servers on which it is replicated.…”