Modelling heterogeneity in many-server queueing systems

Excerpt

In queueing systems, randomness in inter-arrival and service times is a manifestation of the heterogeneity of jobs, i.e. each job has unique characteristics and hence has a different service requirement. Similarly, in a network setting, each job might require a different sequence of processes which motivates the randomized routing mechanism in general Jackson-type and multi-class networks. Even though heterogeneity of jobs is key in the queueing literature, modelling the individual characteristics of servers has not received much attention. For example, in the many-server queue with general inter-arrival and service times, servers are homogeneous, i.e. service times do not depend on the particular server processing the job. This homogeneity assumption does not hold in most applications, especially when servers are humans with varying capabilities. In an empirical study, Gans et al. [6] analyse service time data from call centres and show that agents (servers) in call centres are heterogeneous and service times highly depend on the agent serving the customer. This situation is not limited to the settings with human servers. For example, in computer clusters and especially in cloud computing, the CPU speeds heavily depend on environmental factors such as other system components and heat. A common approach in modelling large-scale systems with heterogeneous service rates is to consider parallel server systems (PSS) with pools where the servers in each pool are identical but service rates can vary between pools (see e.g. [1, 7]). This approach fails to address the individual differences between servers and also assumes that the pool where each server belongs to is known. …