On Mt /Mt /S Type Queue With Group Services

Abstract

We consider M t /M t /S-type queueing model with group services. Bounds on the rate of convergence for the queue-length process are obtained. Ordinary M t /M t /S queue and M t /M t /S type queueing model with group services are studied as examples.

On the Limiting Characteristics for an Inhomogeneous M_t|M_t|S Queue with Catastrophes

“…Let S = 10 12 , λ(t) = 1 + sin 2πt, µ(t) = 3 + 2 cos 2πt, ξ k (t) = ζ k ξ(t), where ξ(t) = 1 − sin 2πt and ζ k = 1 + 1/k. A similar example without catastrophes was considered in [27] and [29].…”

“…Me −at p(0) 1D + LMd 1 a ≤ Mjd j+1 + LMd 1 afor any p(0) = e j , since f(τ ) 1D ≤ d 1 L, and bounds (26),(27) hold.…”

On truncations for weakly ergodic inhomogeneous birth and death processes

“…Our approach also guarantees that we can find limiting characteristics approximately with an arbitrary fixed error, see the detailed discussion by Zeifman et al (2006). Moreover, we can find the limiting characteristics for any number of servers S; see the respective example for S = 10 12 by Zeifman et al (2013b). Arbitrary intensity functions instead of periodic ones can be considered in the same manner.…”

“…λ(t) = 1 + sin2πt, μ(t) = 3 + 2cos2πt. This example and its analogue for a queueing system with group services was considered by Zeifman et al (2013b). Now we consider only an ordinary "classic" queueing model and obtain its main limiting characteristics.…”

Uniform In Time Bounds For “No-Wait” Probability In Queues Of Mt/Mt/S Type

“…Consider the M t /M t /S queue with group services with the arrival intensity λ(t) = 1+sin 2πt and service intensity µ(t) = 3+cos 2πt. This is the same example as in Zeifman and Satin et al (2013). Put d n+1 = 2 n , n ≥ 1.…”