Randomized Scheduling Algorithm for Queueing Networks

📝 Abstract

There has recently been considerable interest in design of low-complexity, myopic, distributed and stable scheduling policies for constrained queueing network models that arise in the context of emerging communication networks. Here, we consider two representative models. One, a model for the collection of wireless nodes communicating through a shared medium, that represents randomly varying number of packets in the queues at the nodes of networks. Two, a buffered circuit switched network model for an optical core of future Internet, to capture the randomness in calls or flows present in the network. The maximum weight scheduling policy proposed by Tassiulas and Ephremide in 1992 leads to a myopic and stable policy for the packet-level wireless network model. But computationally it is very expensive (NP-hard) and centralized. It is not applicable to the buffered circuit switched network due to the requirement of non-premption of the calls in the service. As the main contribution of this paper, we present a stable scheduling algorithm for both of these models. The algorithm is myopic, distributed and performs few logical operations at each node per unit time.

💡 Analysis

There has recently been considerable interest in design of low-complexity, myopic, distributed and stable scheduling policies for constrained queueing network models that arise in the context of emerging communication networks. Here, we consider two representative models. One, a model for the collection of wireless nodes communicating through a shared medium, that represents randomly varying number of packets in the queues at the nodes of networks. Two, a buffered circuit switched network model for an optical core of future Internet, to capture the randomness in calls or flows present in the network. The maximum weight scheduling policy proposed by Tassiulas and Ephremide in 1992 leads to a myopic and stable policy for the packet-level wireless network model. But computationally it is very expensive (NP-hard) and centralized. It is not applicable to the buffered circuit switched network due to the requirement of non-premption of the calls in the service. As the main contribution of this paper, we present a stable scheduling algorithm for both of these models. The algorithm is myopic, distributed and performs few logical operations at each node per unit time.

📄 Content

arXiv:0908.3670v2 [cs.IT] 4 Apr 2010 RANDOMIZED SCHEDULING ALGORITHM FOR QUEUEING NETWORKS By D. Shah J. Shin∗ Massachusetts Institute of Technology There has recently been considerable interests in design of low- complexity, myopic, distributed and stable scheduling policies for con- strained queueing network models that arise in the context of emerg- ing communication networks. Here, we consider two representative models. One, a model for the collection of wireless nodes communi- cating through a shared medium, that represents randomly varying number of packets in the queues at the nodes of networks. Two, a buffered circuit switched network model for an optical core of fu- ture Internet, to capture the randomness in calls or flows present in the network. The maximum weight scheduling policy proposed by Tassiulas and Ephremide [32] leads to a myopic and stable pol- icy for the packet-level wireless network model. But computationally it is very expensive (NP-hard) and centralized. It is not applicable to the buffered circuit switched network due to the requirement of non-premption of the calls in the service. As the main contribution of this paper, we present a stable scheduling algorithm for both of these models. The algorithm is myopic, distributed and performs few logical operations at each node per unit time.

1. Introduction. The primary task of a communication network archi- tect is to provision as well as utilize network resources efficiently to satisfy the demands imposed on it. The main algorithmic problem is that of al- locating or scheduling resources among various entities or data units, e.g. packets, flows, that are contending to access them. In recent years, the ques- tion of designing a simple, myopic, distributed and high-performance (aka stable) scheduling algorithm has received considerable interest in the con- text of emerging communication network models. Two such models that we consider this paper are that of a wireless network and a buffered circuit switched network. ∗Both authors are with the Laboratory for Information and Decision Systems at MIT. DS and JS are with the department of EECS and Mathematics, respectively. Authors’ email addresses: {devavrat, jinwoos}@mit.edu AMS 2000 subject classifications: Primary 60K20, 68M12; Secondary 68M20 Keywords and phrases: Wireless Medium Access, Buffered Circuit Switched Network, Aloha, Stability, Scheduling, Mixing time, Slowly Varying Markov Chain 1 2 SHAH & SHIN The wireless network consists of wireless transmission capable nodes. Each node receives exogenous demand in form of packets. These nodes communi- cate these packets through a shared wireless medium. Hence their simultane- ous transmission may contend with each other. The purpose of a scheduling algorithm is to resolve these contentions among transmitting nodes so as to utilize the wireless network bandwidth efficiently while keeping the queues at nodes finite. Naturally the desired scheduling algorithm should be dis- tributed, simple/low-complexity and myopic (i.e. utilize only the network state information like queue-sizes). The buffered circuit switched network can be utilized to model the dy- namics of flows or calls in an optical core of future Internet. Here a link capacitated network is given with a collection of end-to-end routes. At the ingress (i.e. input or entry point) of each route, calls arriving as per ex- ogenous process are buffered or queued. Each such call desires resources on each link of its route for a random amount of time duration. Due to link capacity constraints, calls of routes sharing links contend for resources. And, a scheduling algorithm is required to resolve this contention so as to utilize the network links efficiently while keeping buffers or queues at ingress of routes finite. Again, the scheduling algorithm is desired to be distributed, simple and myopic. An important scheduling algorithm is the maximum weight policy that was proposed by Tassiulas and Ephremides [32]. It was proposed in the context of a packet queueing network model with generic scheduling con- straints. It is primarily applicable in a scenario where scheduling decisions are synchronized or made every discrete time. It suggests scheduling queues, subject to constraints, that have the maximum net weight at each time step with the weight of a queue being its queue-size. They established through- put optimality property of this algorithm for this general class of networks. Further, this algorithm, as the description suggests, is myopic. Due to the general applicability and myopic nature, this algorithm and its variants have received a lot of attention in recent years, e.g. [20, 5, 30, 27, 4, 28]. The maximum weight algorithm provides a myopic and stable schedul- ing algorithm for the wireless network model. However, it requires solving a combinatorial optimization problem, the maximum weight independent set problem, to come up with a schedule every time. And the problem of finding a maximum weight in

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