Load-dependent service queues with application to congestion control in broadband networks

Abstract

Abstract:We analyze D / G /1 and M / G /1 queues where the service time for an arrival depends on the amount of work in the system upon arrival. The models are motivated by the bit dropping methods (e.g., [12]) as a congestion control in broadband networks. The idea there is to reduce packet (cell) transmission time in case of congestion, while maintaining satisfactory quality of service.To study the load-dependent-service queues, we first derive a functional equation that characterizes the response time for an arbitrary arrival. Then, we employ and extend a technique based on Laguerre functions in [8] to solve the equation. A new recursion is developed in this paper, which significantly simplifies and enhances the applicability of the technique, and makes it easy to program on computers. Numerical examples for packetized voice in a broadband network are included. The enhanced technique is also applicable to other communication and computer systems that can be characterized by similar functional equations.

Transient Analysis of a Tandem Communication Network with Dynamic Bandwidth Allocation having Two Stage Direct Bulk Arrivals

“…To reduce the congestion in buffers, the statistical multiplexing with load dependent strategy has been evolved through bit-dropping and flow control techniques (Sriram et al, (1989), Kin (2002)). However, in bit-dropping and flow control methodologies the focus is on controlling arrival of packets by dropping the least significant bits.…”

“…This type of adjusting the transmission rates depending upon the content of the buffer is known as dynamic bandwidth allocation (DBA). n , n P (t) be the probability that there are n 1 packets in the first buffer and n 2 packets in the second buffer at time t. Then, the difference-differential equations governing the network are ( ) ( ) ( ) ( ) n ,n 1 1 1 2 2 2 n ,n 1 1 n 1,n 1 n n 2 2 n ,n 1 1 n i,n i1 2 n ,n j j2 i 1 j 1 1 2 1 2 2 1 1 2 1 2 1 2 1 2 P (t) n n P (t) n 1 P (t) t (n 1) P (t) P t C P t C P (t) n P (t) P (t) (n 1) P (t) P (t)C t P (t) P (t) P (t) 2 P (t) P (t)C t ∂   =− λ +µ +λ +µ + µ +λ   ∂ (5) ( ) 0 , 0 1 2 0 , 0 2 0 ,1 P ( t ) ( ) P ( t ) P t t ∂ = − λ + λ + µ ∂ (6) with initial conditions 00 i, j P (0) 1; P (0) 0 = = for i, j >0…”

Performance Evaluation of a Communication Network with Dynamic Bandwidth Allocation and Bulk Arrivals

“…As the batch size distribution parameter (b) varies from 10x10 4 packets/sec to 30x10 4 packets/sec, the first buffer, second buffer and the network average content increase from 36813.2 packets to 85897.4 packets, 18069.5 packets to 42162.1 packets and 54882.6 packets to 128059.4 packets respectively when other parameters remain fixed. As the arrival rate of messages (λ) varies from 1x10 4 messages/sec to 3x10 4 messages/sec, the first buffer, second buffer and the network average content increase from 36813.2 packets to 110439.5 packets, 18069.5 packets to 54208.4 packets and 54882.6 packets to 164647.9 packets respectively when other parameters remain fixed at (1,5,25,4,8) for (t, a, b, μ 1, μ 2 ). Similarly when the values of t, λ, a, and b increases, the utilization of node 1 and node 2 were also increasing.…”

“…Statistical multiplexing is one of the major considerations for efficient utilization of the resources. With the statistical multiplexing load dependent communication network models have been generated to accommodate the bit dropping methodologies (Kin K. Leung, 2002). Bit dropping method can be classified as IBD (Input Bit Dropping) and OBD (Output Bit Dropping).…”

Stochastic Control and Analysis of Two-node Tandem Communication Network Model with DBA and Binomial Bulk Arrivals with Phase Type Transmission

“…The idea of bit dropping is to discard certain portion of the traffic such as least significant bits in order to reduce the load in the transmission lines, while maintaining satisfactory quality of service to the end user, whenever there is congestion in buffers. Bit dropping method can be classified as input bit dropping (IBD) and output bit dropping (OBD) respectively (Kin K Leung [6] (2002)). In IBD bits may be dropped when the packets are placed in queue waiting for transmission.…”