Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1512.08609

Performance Analysis of an Unreliable $M/G/1$ Retrial Queue with Two-way Communication

Muthukrishnan Senthil Kumar·Aresh Dadlani·Kiseon Kim
View original source ↗Read source document ↗Export metadata ↓

Abstract

Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an $M/G/1$ retrial queue is investigated where the single server, subject to active failures, primarily attends incoming calls and directs outgoing calls only when idle. The incoming calls arriving at the server follow a Poisson arrival process, while outgoing calls are made in an exponentially distributed time. On finding the server unavailable (either busy or temporarily broken down), incoming calls intrinsically join the virtual orbit from which they re-attempt for service at exponentially distributed time intervals. The system stability condition along with probability generating functions for the joint queue length distribution of the number of calls in the orbit and the state of the server are derived and evaluated numerically in the context of mean system size, server availability, failure frequency and orbit waiting time.

Explore related subjects

cs.NIcs.PF

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Muthukrishnan Senthil Kumar, Aresh Dadlani, Kiseon Kim. 2017-12-26. Performance Analysis of an Unreliable $M/G/1$ Retrial Queue with Two-way Communication. https://doi.org/10.1007/s12351-018-0417-y

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Semord: Learned Semantic-Preserving Placement and Low-Fanout Routing for Distributed Vector Search

Vector databases are increasingly deployed in distributed settings where different users, sites, or domains maintain vector data. Existing vector databases rely on a coordinator to record which shards store which parts of the vector space and to route each query to those shards. In a decentralized setting, peers may join, leave, or move data without a trusted node tracking every change, and outdated routing information can therefore send queries to the wrong peers or require contacting many peers, reducing vector retrieval recall and increasing network latency. We present Semord, a decentralized vector search overlay system that achieves high recall by routing each ANN query to a small set of relevant peers, without relying on a centralized coordinator. Semord addresses this problem by making semantic locality routable: 1) We propose VHash to place semantically related vectors near each other in the overlay key space while avoiding load imbalance, so that each query only needs to contact a small neighborhood of peers for distributed local ANN ranking. 2) We design VecDHT, a communication protocol that maintains decentralized routing, region metadata, churn resilience, and VHash updates under membership and workload changes. Our extensive experiments on a real testbed show that Semord improves recall by more than 15% and reduces contacted peers by over 60% compared with decentralized baselines. Semord also approaches the recall and latency of a centralized oracle baseline while reducing peak peer-local ANN index memory by more than 2X. Controlled large-scale simulations further show that Semord scales across real-world embedding workloads and remains robust under churn for scoped vector retrieval as a decentralized overlay.

cs.NI↗
arXiv2026

Lizard: Bandwidth-Adaptive Real-Time Video Analytics through Content-Aware Packet Discarding at Last-Mile Edge Routers

The timeliness and accuracy of edge-based video analytics can be hindered by drastic reductions in available bandwidth (ABW) at last-mile edge routers, causing prolonged queuing delays. This work proposes Lizard, a system that leverages video-content-aware packet discarding to mitigate the negative effects of drastic ABW degradation that may frequently occur at a last-mile edge router by judiciously discarding packets that contain frame blocks less important to the analytics at the destination. To achieve this, we first devise a frame-block-aware RTP header extension to effectively decouple packet dependencies to encode frame blocks. Second, Lizard uses a priority-based feedback mechanism that dynamically evaluates packet priorities based on relative accuracy impacts. Third, we develop an adaptive phase-transition-based packet discarding strategy at the router to discard packets that represent unimportant blocks. Our evaluation of Lizard shows improvements over existing methods are substantial: 53.2% reduction in latency and 27.1% increase in analysis accuracy.

cs.NI↗
arXiv2026

Flux: Optimal Scheduling of Optical Circuit Switches for LLM Training

Optical Circuit Switching (OCS) offers high bandwidth density and energy efficiency for LLM training, but incurs a non-negligible reconfiguration delay. Prior work typically schedules optical circuit switches independently of compute, using aggregate traffic demand to determine which circuits to provision and when. We argue that this separation creates a fundamental inefficiency: reconfigurations that ignore the compute timeline can stall communication, resulting in low circuit utilization and large buffer requirements. In this paper, we present Flux, a scheduler that optimally schedules optical circuit switches based on the structure of the entire workload. Flux remains effective across a wide range of switching speeds by reusing circuits and amortizing reconfiguration delay behind compute and communication. We show that Flux reduces training iteration time by up to $10\times$ and peak NIC buffer requirements by more than three orders of magnitude compared to traditional periodic schedulers.

cs.NI↗