Admission Policies in Loss Queueing Models with Heterogeneous Arrivals

Abstract

In this paper we consider a loss system where the arrivals can be classified into different groups according to their arrival rate and expected service time. While the standard admission policy consists of rejecting only those customers who arrive when all servers are busy, we address the problem of finding the optimal static admission policy (with respect to a given reward structure) when customers can be discriminated according to the group they belong to, thus customers of some groups might be automatically rejected (even if some servers remain idle) in order to enhance the global efficiency of the system. The optimality of a c\mu -rule is shown, from which finite-time algorithms for the one- and two-server cases are derived.Algorithms, Multichannel Queues, Nonlinear Programming, Optimization

A note on optimal pricing for finite capacity queueing systems with multiple customer classes

“…2 Then, according to Theorem 2 For example, suppose that I = 2, and the relationship between the price p i and the arrival rate λ i (p i ) for class i = 1, 2 is given by…”

“…For example, see Maglaras and Meissner [6] and Talluri and van Ryzin [10]. Within the queueing context, Carrizosa, Conde, and Muñoz-Márquez [2] also use a dimension reduction method in order to analyze an admission control problem for an M/G/s/s queue, but technically their approach and formulation are quite different.…”

Optimal static pricing for a tree network

“…For that case, the system reduces to an M/G/N/N queue, also known as Erlang's loss system. We first give a useful Lemma that is well-known in the literature (see for instance [2,7] and the references therein). However, we provide a short proof that is interesting per se since Equation (4) here below shows that, in an M/G/N/N system, the (discrete) concavity of the nonblocking probability with respect to N follows from the (continuous) convexity of its reciprocal with respect to the offered load y, and vice-versa.…”

“…Though pricing in queueing models with infinite buffers has a long history -see Mendelson [11] for one of the first seminal papers and see Courcoubetis and Weber [4] for more recent references-, the same topic in loss systems has received much less attention. The exception are models for a single link, which includes Courcoubetis and Reiman [3], Lanning et al [8], and Carrizosa et al [2].…”

The facility location problem with Bernoulli demands

“…From a different point of view, when it is accepted that requests that arrive when servers are busy can wait until some server is free, queueing-location models address the minimization of the expected waiting time in the queue or the expected length of the queue. Some references along this line are Marianov and ReVelle [25], Carrizosa et al [10], or Fernández et al [15]. A different methodology to handle these problems comes from Stochastic Programming.…”