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

Source: Akar, Nail - Department of Electrical and Electronics Engineering, Bilkent University

Collections: Engineering