Waiting time distribution in M/D/1 queueing systems

Iversen, Villy Bæk; Staalhagen, Lars

doi:10.1049/el:19991500

Cited by 26 publications

(17 citation statements)

References 2 publications

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“…By the PASTA property [15], the amount of unprocessed work U 1 (x) is identical to the waiting time of a customer when service is first-come, first-served. The waiting time distribution W 1 (x) in a M/D/1 system can be written as [16]: where q is the largest integer less than or equal to x, q = bxc. Finally P L is:…”

Section: Queue Modelmentioning

confidence: 99%

How many smart meters can be deployed in a GSM cell?

Madueno

Stefanović

Popovski

2013

2013 IEEE International Conference on Communications Workshops (ICC)

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Abstract-The need to deploy large number of wireless devices, such as electricity or water meters, is becoming a key challenge for any utility. Furthermore, such a deployment should be functional for more than a decade. Many cellular operators consider LTE to be the single long term solution for wide area connectivity serving all types of wireless traffic. On the other hand, GSM is a well-adopted technology and represents a valuable asset to build M2M infrastructure due to the good coverage, device maturity, and low cost. In this paper we assess the potential of GSM/GPRS/EDGE to operate as a dedicated network for M2M communications. In order to enable M2M-dedicated operation in the near future, we reengineer the GSM/GPRS/EDGE protocol in a way that requires only minor software updates of the protocol stack. We propose different schemes to boost the number of M2M devices in the system without affecting the network stability. We show that a single GSM cell can support simultaneous low-data rate connections (e. g. to smart meters) in the order of 10 4 devices.

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Section: Queue Modelmentioning

confidence: 99%

How many smart meters can be deployed in a GSM cell?

Madueno

Stefanović

Popovski

2013

2013 IEEE International Conference on Communications Workshops (ICC)

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“…In particular, for the Exponential distribution of the packet interarrival times, we apply the M/D/1 steady-state analysis [34] to express probability p that the queuing delay experienced by a packet exceeds Q packets:…”

Section: B Target Utilization Belowmentioning

confidence: 99%

AIST: Insights into queuing and loss on highly multiplexed links

Podlesny

Gorinsky

Rengarajan

2012

2012 IEEE 20th International Workshop on Quality of Service

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Abstract-In explicit or delay-driven congestion control, a common objective is to sustain high throughput without long queues and large losses at the bottleneck link of the network path. Congestion control protocols strive to achieve this goal by transmitting smoothly in the steady state. The discovery of the appropriate steady-state transmission rates is a challenging task in itself and typically introduces additional queuing and losses. Seeking insights into the steady-state profiles of queuing and loss achievable by real protocols, this paper presents an AIST (Asynchronous arrivals with Ideally Smooth Transmission) model that abstracts away transient queuing and losses related to discovering the path capacity and redistributing it fairly among the packet flows on the bottleneck link. In AIST, the flows arrive asynchronously but transmit their packets at the same constant rate in the steady state. For the link with an overprovisioned buffer, our queuing-theoretic analysis and simulations for different smooth distributions of packet interarrival times agree that queuing under AIST with the target utilization of 1 is on the order of the square root of N , where N is the number of flows. With small buffers, our simulations of AIST show an ability to provide bounded loss rates regardless of the number of flows.

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“…Proof: This is a straightforward derivation of classical queuing theory. A numerical method to solve the equation can be found in [14] Combined with Equation 2, we can thus obtain the probability of packet loss as a function of N 6 , τ, and λ.…”

Section: A One Interface Sipnatmentioning

confidence: 99%

A Queueing Theoretic Analysis of Source IP NAT

Westphal¹,

Perkins

2010

2010 IEEE International Conference on Communications

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The number of devices connected to the Internet has outstripped the number of effectively assignable IPv4 addresses. In order to be globally reachable, many devices must share the same IPv4 address; current mechanisms only provide reachability when the device sharing the IPv4 address itself initiates communication. We describe a mechanism to make nodes behind a NAT globally reachable, even when communications are initiated from the global Internet. The intended application of the mechanism, denoted SIPNAT [1], is to allow for the first time bidirectional global reachability of IPv6 addresses by nodes in the global IPv4 Internet, in a scalable manner, thus resolving the major issue associated with IPv4-IPv6 translation.SIPNAT involves filtering flows at the gateway between the IPv4 and IPv6 domain through a combination of DNS request and timing information for the IPv4 initiated connection (the IPv6 to IPv4 connections are performed using typical NAT mechanisms, where the IPv6 domain takes the role of the private address space). We study the performance of the SIPNAT mechanism using queuing theoretic analysis, and show that our SIPNAT model is accurate on actual data traces.

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Waiting time distribution in M/D/1 queueing systems

Cited by 26 publications

References 2 publications

How many smart meters can be deployed in a GSM cell?

How many smart meters can be deployed in a GSM cell?

AIST: Insights into queuing and loss on highly multiplexed links

A Queueing Theoretic Analysis of Source IP NAT

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