 
Summary: Solving MultiRegime Feedback Fluid Queues
H. Emre Kankaya and Nail Akar
Abstract
In this paper, we study Markov fluid queues with multiple thresholds or the socalled multiregime
feedback fluid queues. The boundary conditions are derived in terms of joint densities and for a relatively
wide range of state types including repulsive and zero drift states. The ordered Schur factorization is
used as a numerical engine to find the steadystate distribution of the system. The proposed method is
numerically stable and accurate solution for problems with two regimes and 2 10 states is possible using
this approach. We present numerical examples to justify the stability and validate the effectiveness of
the proposed approach.
I. INTRODUCTION
Markov fluid queues are described by a joint Markovian process {C(t), M(t); t # 0} where {C(t); t #
0} refers to the buffer content at time t and {M(t); t # 0} is an underlying continuoustime Markov
chain that determines the net rate (entry rate minus exit rate or drift) at which the buffer content C(t)
changes. The latter process {M(t); t # 0} is often called the background or the modulating process
of the Markov fluid queue. A key reference on Markov fluid queues is the spectral approach of Anick
et al. [1] for infinite buffer capacities. Tucker [2] extends this analysis to finite fluid queues using the
spectral approach. Kulkarni [3] gives a more recent and extensive overview of Markov fluid queues and
the spectral approach. Ramaswami [4] provides a systematic approach to Markov fluid queues using
the matrix geometric approach. A similar method was proposed by Soares and Latouche [5] for finite
