Exact analysis of transient behavior of finite-capacity MAP-driven queues

This paper studies the workload distribution of a finite-capacity queue driven by a spectrally one-sided Markov additive process (MAP). Our main result provides the Laplace-Stieltjes transform of the workload at an exponentially distributed time, thereby uniquely characterizing its transient distribution. The proposed approach combines several decompositions with established fluctuation-theoretic results for spectrally one-sided Lévy processes. For the special case of Markov-modulated compound Poisson input, we additionally derive results for the idle time and the cumulative amount of lost work. We conclude this paper with a series of numerical experiments.

💡 Research Summary

This paper investigates the transient behavior of a finite‑capacity queue whose input is driven by a spectrally one‑sided Markov additive process (MAP). The authors consider a background Markov chain (J(t)) with a finite state space (\mathcal{D}={1,\dots,d}). When the chain is in state (i), the workload evolves according to a spectrally positive Lévy process (Y_i) (no negative jumps). In addition, each transition (i\to j) may bring an extra job of size (B_{ij}) with Laplace–Stieltjes transform (\mathcal{B}_{ij}(\cdot)). The workload process (V(t)) is doubly reflected at the lower bound 0 and the upper bound (K>0), i.e. it satisfies the Skorokhod problem
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