14.1 Introduction

Load-dependent devices (LD) are used to model service centers where the service rate varies with the number of customers present in its queue. Examples of servers with variable service times, depending on the current load, abound in modern computer-based systems. For example, multimedia traffic uses variable grades of service to control congestion. In congestion control mechanisms for continuous bit rate (CBR) traffic in broadband networks, bit dropping methods are used to discard certain portion of the traffic, such as the least significant bits, in order to reduce the transmission time (i.e., the service time) [11]. Thus, when a system has a large number of requests queued, new arrivals are forced to receive low-grade service, which shortens the service time. Local area networks (e.g., Ethernet) have been modeled by LD devices [13], representing the fact that Ethernet efficiency depends on the number of computers trying to transmit data. Disk servers may also be modeled by load-dependent devices [15]. When there are multiple requests queued up at the disk, the seek time to the nearest request increases inversely with the number of queued requests. Thus, the effective disk service rate varies with the number of queued requests. Queuing models with load-dependent devices capture the dynamic nature of various components of computer systems.

A queuing model may represent different types of resources, according to whether there is queuing and whether the average service rate, m(n), depends on the current queue length n or not. As described in previous chapters, load-independent (LI) devices represent resources where there is queuing but the average service rate does not depend on the load (i.e., m(n)=m for all values of n). In contrast, load-dependent devices are used to represent resources where there is queuing and the average service rate depends on the load (i.e., m(n) is a function of n), as shown in Figure 14.1.

Figure 14.1. Service rate function for LI and LD devices.


This chapter focuses on the solution of queuing models with load-dependent service times. The MVA method [16] is extended to handle the existence of load-dependent (LD) devices. A motivating example is presented, followed by single and multiple class LD solution algorithms. Closed and open models are allowed. At the end of the chapter, the Flow Equivalent Server Method is introduced. This method is useful for reducing the size of a performance model by replacing an entire subnetwork of a QN by a single equivalent LD device.

Performance by Design. Computer Capacity Planning by Example
Performance by Design: Computer Capacity Planning By Example
ISBN: 0130906735
EAN: 2147483647
Year: 2003
Pages: 166

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