Fluid Models of Parallel Service Systems under FCFS

Abstract

We study deterministic fluid approximations of parallel service systems operating under first come first served policy (FCFS). The condition for complete resource pooling is identified in terms of the system structure and the customer service times. The static planning linear programming approach (Harrison and Lopez [22]) is used to obtain a maximum throughput compatibility tree and to show that FCFS using this compatibility tree is throughput optimal. We investigate matching rates and show by Hotelling's T 2 -test and simulation that they are dependent on the service time distribution.

Design heuristic for parallel many server systems

“…An incomplete list would include an early study [14]; applications to manufacturing and supply chain management [28,23], applications to call centers and internet service systems [12,17,24,29], attempts to find optimal policies, mainly for small graph systems [31,8,6,7,13,26], heavy traffic and fluid approximations [18,19], and many server scaling [15,16]. Most relevant to our current paper are [11,5,25,22].…”

“…It is the calculation of the matching rates, how many customers of type c i are served by servers of type s j under FCFS-ALIS, which is intractable, and may depend on the entire shape of the service time distributions. Matching rates can be calculated for some types of graphs [25,22], and they can also be calculated for general bipartite graphs when arrivals are Poisson, service rates depend only on the servers, and services are exponential [5], but not otherwise. However, matching rates can be calculated for the much simpler and very tractable FCFS infinite bipartite matching model [9,4,3].…”

“…Such minimization will usually be achieved by a tree compatibility graph, for which matching rates are easily computed (cf. [22]). Rather it is to start from a given compatibility graph, and obtain designs which achieve resource pooling and balance of service.…”