Samuel P. Morgan

Input Versus Output Queueing on a Space-Division Packet Switch

Two simple models of queueing on an N \times N space-division packet switch are examined. The switch operates synchronously with fixed-length packets; during each time slot, packets may arrive on any inputs addressed to any outputs. Because packet arrivals to the switch are unscheduled, more than one packet may arrive for the same output during the same time slot, making queueing unavoidable. Mean queue lengths are always greater for queueing on inputs than for queueing on outputs, and the output queues saturate only as the utilization approaches unity. Input queues, on the other hand, saturate at a utilization that depends on N , but is approximately (2 -\sqrt{2}) = 0.586 when N is large. If output trunk utilization is the primary consideration, it is possible to slightly increase utilization of the output trunks-upto (1 - e^{-1}) = 0.632 as N \rightarrow \infty -by dropping interfering packets at the end of each time slot, rather than storing them in the input queues. This improvement is possible, however, only when the utilization of the input trunks exceeds a second critical threshold-approximately ln (1 +\sqrt{2}) = 0.881 for large N .

General Solution of the Luneberg Lens Problem

The general solution is obtained for the index of refraction of a variable‐index, spherical lens which will form perfect geometrical images of the points of two given concentric spheres on each other. One conjugate sphere is assumed to be outside the lens or at its surface, while the other may be either inside, outside, or at the surface. If one of the spheres is of infinite radius, the lens will focus a parallel beam perfectly at a point on the other sphere.It is shown that the index of refraction may be specified arbitrarily, subject to two simple conditions, in an outer shell of any desired thickness less than the radius of the lens. The index of the central portion is then expressed in terms of a function which is tabulated, and of an integral involving the index of the outer shell. Some properties of the general solution are discussed, and various special solutions are derived.

SMART retransmission: performance with overload and random losses

Feedback flow control, in conjunction with limited buffering in the network, inevitably leads to packet loss. Effective congestion control requires not only effective flow control but also a good retransmission strategy. We present a new retransmission strategy called SMART that combines the best features of the traditional go-back-n and selective-retransmit strategies. We show, first, that go-back-n retransmission with static window flow control leads to congestion collapse when the nominal load exceeds the link capacity. Second, we can avert congestion collapse by replacing go-back-n with SMART retransmission, even with static window flow control. Third, SMART retransmission, when combined with packet-pair rate-based flow control, performs extremely well, both when losses are due to buffer overflows and when losses are random.

Queueing disciplines and passive congestion control in byte-stream networks

The performance is compared of first-in-first-out and round-robin packet service disciplines at the trunk nodes of byte-stream networks, including priority service for single-packet messages. Delay and throughput characteristics are surveyed as a function of traffic mix, packet size, traffic intensity, and the ratio of trunk speed to access line speed. Exact and approximate analyses are compared with the results of simulations. Under normal traffic conditions, most disciplines will give acceptable mean delay if the ratio of trunk speed to access line speed is sufficiently high. Under congestion, round-robin disciplines have better fairness properties than first-in-first-out disciplines, in that they protect well-behaved users against hogs.<<ETX>>

Statistics of mixed data traffic on a local area network

Abstract We have analyzed a weeks worth of data traffic on a DATAKIT∗ Virtual Circuit Switch network at AT&T Bell Laboratories. The network includes 5 nodes connecting 22 host computers and 226 terminals, with trunks to nodes elsewhere at Bell Laboratories. Users are predominantly researchers using the UNIX† operating system via teletypewriter terminals and diskless work stations at 9.6 kb/s. Comparable fractions of the traffic are generated by terminal-to-host calls, by indirect logins, by inteactive remote command executions, and by host-to-host file transfers. We display histograms representing the distributions of interarrival times and call lenghts associated with the various types of callsm and the distributions of transmissions bursts in individual calls. We characterize typical distributions by their means and coefficients of variation, and propose a model for time-sharing traffic which depends on a relatively small number of parameters and statistical distributions.

Queuing disciplines and passive congestion control in byte-stream networks

The mean delay and throughput characteristics of various trunk queuing disciplines of the FIFO (first in, first out) and round-robin types for byte-stream data networks are investigated. It is shown that, under normal traffic, high-speed trunks substantially reduce queuing delays. Almost any queuing discipline will give acceptable delay if the backbone network is sufficiently faster than the access lines. In the absence of high-speed trunks, both the packet FIFO and the round-robin discipline can be augmented with a priority queue that expedites single-packet messages, which may carry network control signals or echoplex characters. In FIFO-type disciplines, the mean delays of messages that do not go through the priority queue depend on the overall message length distribution. A sprinkling of very long messages can significantly increase the mean delays of other messages. In disciplines of round-robin type, the mean delay of each message type is not affected by the presence of very long messages of other types. >

Window flow control on a trunked byte-stream virtual circuit

The throughput versus window-size behavior of the sliding window protocol is studied on a trunked byte-stream virtual circuit. For the case studied, the node service discipline is processor sharing, background traffic is Poisson with exponentially distributed message lengths, propagation times are a significant fraction of the total delay, and the channel error rate is negligible. Analytic models are compared to the results of simulation. For small windows, the throughput is controlled by the ratio of window size to roundtrip propagation time. For large windows, the throughput is controlled by the background traffic level, the number of hops, and the ratio of window size to background message length. >

Hemispherical concentrators and spectral filters for planar sensors in diffuse radiation fields

A dielectric hemisphere of refractive index N can act as an N(2) concentrator of isotropic diffuse radiation under appropriate conditions. We give an analytic expression for the gain of a concentrator of arbitrary radius, neglecting surface reflections, and numerical methods for calculating the gain when the surface transmissivity is an arbitrary function of incidence angle. The theory is applied to the design of multilayer spectral filters for hemispherical concentrators. When an appropriate wavelength shift is incorporated into the design process, an 11-layer, coupled-cavity spectral filter on the surface of a hemisphere of index 1.5 shows excellent bandpass performance with a concentrator radius as small as 3 times the sensor radius. This concentrator-filter combination shows a peak response of 97% of the ideal N(2) response at 950 nm, together with a FWHM of 55 nm.

Mean message delays for two packet-FIFO queueing disciplines

Expressions are derived for the mean message delay, as a function of message length, when data messages of different lengths arrive asynchronously at a trunk and are divided, as they come in, into packets of some maximum length. The packets of different messages are intermingled and are put onto the trunk either from a single first-in-first-out (FIFO) queue, or from a high-priority and a low-priority queue for single-packet and multiple-packet messages, respectively. The results are compared to the case in which messages enter service in order of arrival and each message is served to completion without interruption, so that the mean message delay is independent of message length. >

The UNIX Operating System: A Model for Software Design.

The UNIX operating system, a general-purpose time-sharng system, has, without marketing, advertising, or technical support, become widely used by universities and scientific research establishments. It is the de facto standard of comparison for such systems and has spawned a small industry of suppliers of UNIX variants and look-alikes. This article attempts to uncover the reasons for its success and to draw some lessons for the future of operating systems.