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...ed on its ability to partially solve hard queueing problems (i.e., in terms of bounds), SNC is justifiably proclaimed as a valuable alternative to the classical queueing theory (see Ciucu and Schmitt =-=[4]-=-). At the same time, SNC is also justifiably questioned on the tightness of its bounds. While the asymptotic tightness generally holds (see Chang [2], p. 291, and Ciucu et al. [1]), doubts on the boun...

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...tant capacity node provides a stochastic service curve C ·t with bounding function F̄L max(t)(x). Unfortunately, Lmax(t) is non-decreasing with t, implying that F̄Lmax(t)(x) may approach 1 as t grows =-=[9]-=-3. Consequently, using F̄Lmax(t) as a bounding function is meaningless. The problem becomes even more challenging when there is cross traffic. First, in order to apply the leftover service property to...

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...eing theory. The main approaches to formulate the SNC can be found in [11, 2, 6, 8]. Recently, the dust has settled and the relation between these different flavours of SNC has been understood better =-=[5]-=-. The SNC turned out to be very useful in many applications; here we name a few less obvious use cases: overloaded FIFO queues [3], power grid [16], airplane cabin network [12]. Despite all this progr...

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... show that this setting allows a simple handling of multiplexing and scheduling: whereas multiplexing of several sources results in multiplication of the corresponding martingales, per-flow analysis in a scheduled system can be done by shifting the martingales to a certain point in time. Applying this calculus to Markov Arrival Processes, it is shown that the performance bounds can become reasonably tight. 1. INTRODUCTION The Stochastic Network Calculus (SNC) arises as an alternative to classical queueing theory. Its main advantage is its amenability to scheduling and multi-hop scenarios (see [4]). However, the price of this advantage is that the resulting performance metrics, like the distribution of the stationary queue size and the delay, are not computed exactly but only estimated via upper and/or lower bounds. As most of these bounds in the existing literature are based on techniques from large deviations theory, which are known to render loose bounds (see, e.g., [2]), the relevance of SNC itself is often questioned. This looseness stems from the following fact: When computing bounds on some performance metrics (e.g., buffer overflow probability), the crucial point is to estimate...

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...ues for the event {A(s, t) − G(t − s)} for each trajectory and any time t, and (2) use the complementary cumulative distribution function (CCDF) of the sample set as a bounding function for Eq. (2.9) =-=[12]-=-. Markovian arrival using Network Calculus Sometimes an arrival model is given instead of a measurement set. One of the most general and widely-used models is the multi-state Markovian (MSM) fluid flo...

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... are discussed. CHAPTER 1 Introduction Stochastic Network Calculus (SNC) has matured in recent years to provide an alternative method for performance analysis of stochastic queueing systems (see e.g. =-=[14, 12, 8]-=-). Many results from the deterministic network calculus (DNC) have been transferred into the stochastic domain, some have been rather immediate some have required considerable effort (e.g., deriving t...