Following the relationship between the t. As an example of Lemma 1. Wayne Wheeler there for their patience, support, and help. Tradeoff must be considered between the feasibility for the analysis of performance bounds, the usefulness of performance bounds, and the ease of their numerical calculation. The stochastic service curve model may be viewed as a further development of the weak stochastic service curve model since without additional constraint the latter does not support the concatenation property, as will be shown in the next chapter.
If no bn satisfying 7. Considering the wireless system as shown in Problem 4. For stochastic network calculus, they have also been studied in the literature, although in most cases separately. One is based on the concept of a stochastic strict service process due to impairment, introduced in Section 4. Networking, 15 6 :1442—1453, December 2007.
Stochastically bounded burstiness for communication networks. Consider a system S with input A. Because of this, a Gaussian process is often used to approximate the cumulative arrival process. In wireless networks, the capacity of a wireless channel varies over time in a random manner due to channel impairment, contention, and other causes. Suppose the backlog of A in the system is upper-bounded by b for all times. The independence assumption is generally required between arrival and service processes.
It was shown in Section 5. Find the non-conformance probability for F1. However, while in c- ventional queuing theory an arrival process is typically characterized by the inter-arrival times of customers and a service process by the service times of customers, the arrival process and the service process are modeled in n- work calculus respectively by some arrival curve that maybe probabilis- cally upper-bounds the cumulative arrival and by some service curve that maybe probabilistically lower-bounds the cumulative service. Networking, 3 3 :226—244, June, 1995. Another constraint that will also often be used in this book is to assume ¯ i.
Determining end-to-end delay bounds in heterogeneous networks. If the input has a t. In the meantime, researchers have studied stochastic QoS performance for specific schedulers. In addition, we introduce strict stochastic server to help find the stochastic service curve of a stochastic server, which characterizes the service of the server by two stochastic processes: an ideal service process and an impairment process. Submitted for publication, January 2008. As a special case, the following result follows from Corollary 5. For the same mapping function of random variables, if these random variables are independent, the following result holds see, e.
Consider a system S with input A. Client requirements for real-time communication services. While part ii can also be proved from Theorem 4. Synchronization and Linearity: An Algebra for Discrete Event Systems. Interestingly, the bounding function shown as the right-hand side of 3.
Suppose the input has an ¯ i. Note that the right-hand side of 6. In general, the backlog may not be deterministically upper-bounded. Assume the system provides a service envelope process Sˆ to the aggregate, and A2 has a stochastic envelope process Aˆ2. . Statistical analysis of the generalized processor sharing scheduling discipline. Finally, based on the relationship between the t.
We now consider that the input is modeled with a v. Let A be the aggregate. There is a lot of work including an elegant theory under the name of network calculus focusing on analysis of deterministic worst case QoS performance bounds. A central-limit-theorem-based approach for analyzing queue behavior in high-speed networks. In particular, stochastic arrival curves for spectrum sensing error processes are derived firstly, based on which stochastic service curve for each class of users is obtained under different retransmission schemes, including without retransmission, retransmission until success and maximum-N-times retransmission. In contrast, the stochastic service curve model may generally have a time-dependent bounding function.