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...rm stands for factorization to individual componentssor stations. This product form result is related to product form resultssin the extensive literature on queueing networks (cf. [3], [4], [7],s[8], =-=[12]-=-, [26]), but has as such not been reported or recognized forsthe system under study. It can be shown that it conceptually fits in thesframework of reversibility (cf. [12]) or of job-local-balance (cf....

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...ing random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , [13] , [14] , [15] ,s[16], [20], [21], =-=[22]-=-, [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions (e.g. [2], [16], [23]).sParticularizing...

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...oldswhich here would read as: "The steady state distribution as seen by asnode upon think time completion is given by (4.2) for the system withoutsthat node". The well-known mean value algorithm (cf. =-=[19]-=-) to efficiently compute performance measures can thus be applied. A computational approach to compute the normalizing constant based upon a statistlcal mechanics technique can be found in [18].s5. In...

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...thesnumber of these using trunkgroup i, and MA the number of trunks instrunkgroup i, we can usesA(h H)s1 if ̂s(H U h) < Mt for all is0 otherwise .sExample 2.4. (Synchronous servicing) (cf. [6], [10], =-=[11]-=-). As a typical feature of digital transmissions, a transmission may use several timesslots from a limited number of M time slots. The following figure visualizes that a type-i message simultaneously ...

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...nds for factorization to individual componentssor stations. This product form result is related to product form resultssin the extensive literature on queueing networks (cf. [3], [4], [7],s[8], [12], =-=[26]-=-), but has as such not been reported or recognized forsthe system under study. It can be shown that it conceptually fits in thesframework of reversibility (cf. [12]) or of job-local-balance (cf. [8],s...

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...uetionsVarious packet or circuit switching random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , =-=[13]-=- , [14] , [15] ,s[16], [20], [21], [22], [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions ...

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...1 - 1. IntroduetionsVarious packet or circuit switching random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. =-=[2]-=- , [10] , [13] , [14] , [15] ,s[16], [20], [21], [22], [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their vario...

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...ndom access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , [13] , [14] , [15] ,s[16], [20], [21], [22], =-=[23]-=-, [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions (e.g. [2], [16], [23]).sParticularizing to CS...

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...replace N(h) be the set ofsneighbors that is either transmitting or hearing. Clearly, these two-hopsinteractions can be extended to multi-hop interactions.s- 5 - Example 2.3. (Circuit switching) (cf. =-=[3]-=-, [20]). A circuit switchingstransmission may typically have a structure of the formswhere messages from a particular source Si are to be transmitted along asparticular path T?t to a destination DA . ...

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...rcuit switching random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , [13] , [14] , [15] ,s[16], =-=[20]-=-, [21], [22], [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions (e.g. [2], [16], [23]).sPar...

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...es, NL (H) thesnumber of these using trunkgroup i, and MA the number of trunks instrunkgroup i, we can usesA(h H)s1 if ̂s(H U h) < Mt for all is0 otherwise .sExample 2.4. (Synchronous servicing) (cf. =-=[6]-=-, [10], [11]). As a typical feature of digital transmissions, a transmission may use several timesslots from a limited number of M time slots. The following figure visualizes that a type-i message sim...

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...s. A product form stands for factorization to individual componentssor stations. This product form result is related to product form resultssin the extensive literature on queueing networks (cf. [3], =-=[4]-=-, [7],s[8], [12], [26]), but has as such not been reported or recognized forsthe system under study. It can be shown that it conceptually fits in thesframework of reversibility (cf. [12]) or of job-lo...

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...interruptions (see example 3.6) can so be modeled.sRemark 2.6. The assumption of a restarting think or holding time uponsblocking is common for communication systems (cf. [6], [10], [11], [15],s[16], =-=[17]-=-, [20], [27]). For an exponential think or holding time, itscoincides with interrupting this time to evolve if the idle or busysstatus respectively is currently not allowed to change (cf. [17]).sRemar...

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... or circuit switching random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , [13] , [14] , [15] ,s=-=[16]-=-, [20], [21], [22], [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions (e.g. [2], [16], [23]...

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...ct form stands for factorization to individual componentssor stations. This product form result is related to product form resultssin the extensive literature on queueing networks (cf. [3], [4], [7],s=-=[8]-=-, [12], [26]), but has as such not been reported or recognized forsthe system under study. It can be shown that it conceptually fits in thesframework of reversibility (cf. [12]) or of job-local-balanc...

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...), but has as such not been reported or recognized forsthe system under study. It can be shown that it conceptually fits in thesframework of reversibility (cf. [12]) or of job-local-balance (cf. [8],s=-=[9]-=-), provided appropiate conditions are met. However, sufficiënt conditions in terms of concrete system protocols are hereby left open andsnot obvious. To this end, a general invariance condition will b...

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...product form stands for factorization to individual componentssor stations. This product form result is related to product form resultssin the extensive literature on queueing networks (cf. [3], [4], =-=[7]-=-,s[8], [12], [26]), but has as such not been reported or recognized forsthe system under study. It can be shown that it conceptually fits in thesframework of reversibility (cf. [12]) or of job-local-b...

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... packet or circuit switching random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , [13] , [14] , =-=[15]-=- ,s[16], [20], [21], [22], [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions (e.g. [2], [16...

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...es"averaged out" leading to expression (4.2) with ah and rh representings"averaged" means. Multi levels may reflect for instance different interrupted phases of a transmission.s- 15 - 4. Similarly to =-=[25]-=-, also the "arrival theorem" can be shown to holdswhich here would read as: "The steady state distribution as seen by asnode upon think time completion is given by (4.2) for the system withoutsthat no...

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...hus be applied. A computational approach to compute the normalizing constant based upon a statistlcal mechanics technique can be found in [18].s5. In various Standard ways (e.g. by letting N-*» as in =-=[1]-=- or by including a "dummmy node" as in [8]), similar results can be provided tosmodel "infinite or open" transmission systems with Poissonian inputs.sProof of theorem 4.1.sWe need to verify the global...

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...to multihop random access 'sschemes which take into account the well-known "hidden terminal problem". Relaxations to non-exponential packet lenghts (cf. [2]) and transmitter dependent parameters (cf. =-=[5]-=-) were also- established. However,stransmissions are still assumed to be exponential and several randomsaccess schemes of practical interest are not yet covered.sThis paper aims to show that a concept...

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... IntroduetionsVarious packet or circuit switching random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , =-=[10]-=- , [13] , [14] , [15] ,s[16], [20], [21], [22], [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various exte...

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...s- 4 - Throughout let H - {h-L , . .. ,1̂ } and denote by H + h the state in whichsnode h is added (+) or deleted (-) as a busy node.sExample 2.1. (Interference graph; Standard CSMA) (cf. [14], [16], =-=[18]-=-,s[20]). Let the nodes in a graph represent transmitters with the restriction that adjacent nodes cannot transmit at the same time. Let N(h) besthe set of all neighbors of node h. Then the above descr...

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...switching random access schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , [13] , [14] , [15] ,s[16], [20], =-=[21]-=-, [22], [23], [27]). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions (e.g. [2], [16], [23]).sParticula...

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...a counterexample with O and 1 values orsone can recursively calculate P(H) as based upon "basic" paths orscycles. (Related resul ts along this line can be found in [7], [8] ands[12]).s3. Similarly to =-=[24]-=-, the above results can be extended to allow different levels of think and holding times for a node. These levels can bes"averaged out" leading to expression (4.2) with ah and rh representings"average...

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...ccess schemes for computer, broadcasting or telecommunication networks have been introduced andsinvestigated over the last decades (cf. [2] , [10] , [13] , [14] , [15] ,s[16], [20], [21], [22], [23], =-=[27]-=-). Most notably among these are thesALOHA (e.g. [13], [20]) and CSMA (e.g. [13], [14], [20]) packetsswitching protocols and their various extensions (e.g. [2], [16], [23]).sParticularizing to CSMA-pro...