Stochastic network calculus is a theory for stochastic service guarantee analysis of computer communication networks. In the current stochastic network calculus literature, its traffic and server models are typically based on the cumulative amount of traffic and cumulative amount of service respectively. However, there are network scenarios where the applicability of such models is limited, and hence new ways of modeling traffic and service are needed to address this limitation. This paper presents time-domain models and results for stochastic network calculus. Particularly, we define traffic models, which are based on probabilistic lower-bounds on cumulative packet inter-arrival time, and server models, which are based on probabilistic upper-bounds on cumulative packet service time. In addition, examples demonstrating the use of the proposed time-domain models are provided. On the basis of the proposed models, the five basic properties of stochastic network calculus are also proved, which implies broad applicability of the proposed time-domain approach.
Deep Dive into Stochastic Service Guarantee Analysis Based on Time-Domain Models.
Stochastic network calculus is a theory for stochastic service guarantee analysis of computer communication networks. In the current stochastic network calculus literature, its traffic and server models are typically based on the cumulative amount of traffic and cumulative amount of service respectively. However, there are network scenarios where the applicability of such models is limited, and hence new ways of modeling traffic and service are needed to address this limitation. This paper presents time-domain models and results for stochastic network calculus. Particularly, we define traffic models, which are based on probabilistic lower-bounds on cumulative packet inter-arrival time, and server models, which are based on probabilistic upper-bounds on cumulative packet service time. In addition, examples demonstrating the use of the proposed time-domain models are provided. On the basis of the proposed models, the five basic properties of stochastic network calculus are also proved, w
Stochastic network calculus is a theory dealing with queueing systems found in computer communication networks [1] [2] [3] [4]. It is particularly useful for analyzing networks where service guarantees are provided stochastically. Such networks include wireless networks, multiaccess networks and multimedia networks where applications can tolerate some certain violation of the desired performance [5].
Stochastic network calculus is based on properly defined traffic models [6][3][4] [7][8] [9] and server models [3] [4]. In the existing models of stochastic network calculus, an arrival process and a service process are typically modeled by some stochastic arrival curve, which probabilistically upper-bounds the cumulative amount of arrival, and respectively by some stochastic service curve, which probabilistically lower-bounds the cumulative amount of service. In this paper, we call such models space-domain models. Based on the spacedomain traffic and server models, a lot of results have been derived for stochastic network calculus. Among the others, the most fundamental ones are the five basic properties [3] [4]: (P.1) Service Guarantees including delay bound and backlog bound; (P.2) Output Characterization; (P.3) Concatenation Property; (P.4) Leftover Service; (P.5) Superposition Property. Examples demonstrating the necessity of having these basic properties and their use can be found [3] [4].
Nevertheless, there are still many open research challenges for stochastic network calculus, and a critical one is time-domain modeling and analysis [4]. Timedomain modeling for service guarantee analysis has its root from the deterministic Guaranteed Rate (GR) server model [10], where service guarantee is captured by comparing with a (deterministic) virtual time function in the time-domain. This time-domain model has been extended to design aggregate-scheduling networks to support per-flow (deterministic) service guarantees [11] [12], while few such results are available from spacedomain models. Other network scenarios where timedomain modeling may be preferable include wireless networks and multi-access networks.
In wireless networks, the varying link condition may cause failed transmission when the link is in ‘bad’ condition. The sender may hold until the link condition becomes ‘good’ or re-transmit. For such cases, it is difficult to directly find the stochastic service curve in the space-domain because we need to characterize the stochastic nature of the impaired service caused by the ‘bad’ link condition. A possible way is that we use an impairment process [3] to characterize the impaired service. However, how to define and find the impairment process arises another difficulty. Even though we can define an impairment process, we may first convert the impairment process into some existing stochastic network calculus models, and then further analyze the performance bounds. The obtained performance bounds may become loose because of such conversion. If we characterize the serivce process in the time-domain, we can use random variables to represent the time intervals when the link is in ‘bad’ condition. Analyzing the stochastic nature of such random variables would be easier. In addition, this way can avoid the difference introduced by the intermediate conversion.
In contention-based multi-access networks, backoff schemes are often employed to reduce collision occuring. Because the backoff process is characterized by backoff windows which may vary with the different backoff stages, it is quite cumbersome for a space-domain server model to characterize the service process with the consideration of the backoff process. This also prompts the possibility of characterzing the service process in the time-domain. Having said this, however, how to define a stochastic version of the virtual time function and how to perform the corresponding analysis are yet open [4].
The objective of this paper is to define traffic models and server models in the time-domain and derive the corresponding five basic properties for stochastic network calculus. Particularly, we define traffic models that are based on probabilistic lower bounds on cumulative packet inter-arrival time. Also, we define server models that are based on some virtual time function and probabilistic upper bounds on cumulative packet service time.
In addition, we establish relationships among the proposed time-domain models, and the mappings between the proposed time-domain models and the existing spacedomain models. Furthermore, we prove the five basic properties based on the proposed time-domain models.
The remainder is structured as follows. Sec. II introduces the mathematical background and fundamental space-domain models and relevant results of stochastic network calculus. In Sec. III, we first introduce the time-domain deterministic traffic and server models, and then extend them to stochastic versions. In addition, the relationships among them as well as wit
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